(I answered part of a related question you asked elsewhere. Here is the rest)
Firstly, I unfortunately disagree with many of your comments above and the conclusions you draw from them.
I find your classification of the three types confusing. I propose to relabel the categories as follows for the sake of my comments below:
Category A. Pertubatively renormalisable: All divergences can be absorbed by renormalising a finite number of parameters of the theory while still maintaining all the desired symmetries.
Category B. Power Counting renormalisable: The superficial degree of divergence of graphs
is investigated to see if the divergence structure is likely to be manageable. If the couplings are all of positive mass dimension then there is hope that the theory is manageable and also that it might fall under category A (but that requires detailed proof).
Category C. Wilson renormalisation. Here one uses a cutoff, and studies the RG flow of the theory. Effective low energy theories are of interest in condensed matter and also in high energy physics.
Now some comments which address your questions, and also comments on some of you comments that I disagree with:
a. QED has a Landau pole in perturbation theory. No one knows what happens to it non-perturbatively. Indeed long before you reach the Landau pole, the approximation you used to get that pole breaks down.
b. The Standard Model of particle physics, which is still the best experimentally tested theory of the strong, weak and electromagnetic interactions, falls under categories A and B. It can also be studied under category C if you wish, and people have done that to get low energy effective theories for particular applications (see below).
c. I do not know what "nonpertubatively renormalisable" could mean. Any expansion of the quantum theory will be perturbative in some parameter or another. If not the coupling "g", the large N etc. (Unless maybe if you put it on a lattice and study it there...i am not sure even then).
d. The physical meaning of Category A and why its a big deal:
If a theory is in category A then it is in some sense self-contained. After fixing a finite number a parameters you can answer many more questions to arbitrary degree of accuracy. Eg the anomalous magnetic moment of the electron agrees with experiment to 10 significant figures. Many many loops calculated by Kinoshita and company over decades.
It has been reported as the best verified prediction in the history of physics. So we must be doing something right here. I think we need to pause a few seconds to appreciate this achievement of mankind.
To continue. Historically, the Category A requirement was one of the crucial guiding principle in constructing the Standard Model (see Nobel acceptance speech by Weinberg). The theory that was constructed predicted many new particles that had not yet been observed. Many Nobel prizes were awarded based on the predictions that came true.
It is always possible to cook up some theory to explain known facts, but to predict something and to find it come true, time and again, is exceptional.
So, a self-contained predictive structure that agrees with Nature. That is what category A is about. That is why it is in the text books.
Physically, it means that Category A theories are not sensitive to the unknown physics at the arbitrarily large cut off you have chosen (taken to infinity eventually) and whose ignorance is partially absorbed in the renormalisation parameters. In this sense category A theories are not different physically from Category C investigations. Its just that in Category A people tried to push the cutoff to infinity and they succeeded.
But the enterprise could have failed badly, then it would have been forgotten and we would have been trying something else (by the way, people were trying something else in the old days, like S-matrix approach and bootstrap when they were groping in the dark...Google it).
e. The fact that it worked tells us that any new physics beyond the Standard Model is at a much higher energy than what we had explored previously. The LHC is trying now to find the potential new physics. Which leads me to the next point.
f. The Standard Model is probably not the end of the story. In fact with the modern perspective that all theories are in some sense effective theories, even the standard model, you can now add non-renormalisable terms to account for potential high energy physics that we have not yet seen. These extra terms you add are constrained by the success of what we have already seen. Weinberg's book and many other places discuss this.
So far no new physics beyond that predicted by the Standard model has been seen at LHC (though some people think that the smallness of the likely neutrino masses might be a hint of something beyond the horizon).
g. The Wilsonian perspective, that all theories are effective theories is wonderful. After all, we cant claim to know what is beyond what we have seen so far. His approach was immensely successful in condensed matter physics, and as I mentioned in points above, it is also adopted by many particle physicists.
But instead of "integrating our higher degrees of freedom" which is difficult technically (the top down approach) and in practice (what is your top theory? string theory? something else?), most people start at the bottom (renormalisable theory) and add non-renormalisable terms as i mentioned above.
In summary:
Category A is the crowning glory of particle physicists. It still provides guidance on the construction of extensions of particle physics theories.
Category C is the modern perspective on what theories are. But as i said above, it doesn't conflict with Category A which was an ambitious programme that somehow succeeded.
There are some language differences between those who are in the Category A camp and those who are in the Category C camp, but I believe its simply a matter of history and convenience.
I recommend the book by Zinn Justin which I believe covers all the Categories: A, B and C. Its a 1000 odd pages, with all details worked out, though the presentation is a bit terse. (I have not read it but flipped through it many years ago). The author is a renowned practitioner in the field of renormalisation with many original contributions.
Like you said, we can include gravity perturbatively in the framework of low-energy effective QFT, as reviewed in reference 1. This works because gravity is extremely weak at the energies that characterize modern particle-physics experiments. But the interest in quantum gravity revolves around nonperturbative/high-energy/strong-field issues, like the holographic principle and the informaion-loss paradox, both of which were already known in the 1970s (references 2,3,4) and were surely on Distler's mind in 1982.
Thanks to universality, very different theories can become indistinguishable from each other at sufficiently low resolution. Low-energy experiments can only fix the first several terms in the lagrangian on which perturbation theory is based. That's what allows us to include gravity in the Standard Model in the sense of low-energy effective theory (reference 1), and I'm guessing this was also the basis for Georgi's assertion. Terms of higher order in the cutoff are not resolved, so we cannot attack the interesting questions about quantum gravity — which are nonperturbative/high-energy/strong-field — by extrapolating upward from the low-energy effective theory.
Even if it was fair at the time, Georgi's "waste of time" judgement is obsolete now, because now we have approaches to studying quantum gravity that don't rely on extrapolating upward from a low-energy effective theory. Perturbative string theory is tightly constrained by numerous anomaly cancellation requirements, which are nonperturbative. Fully nonperturbative formulations like AdS/CFT are also available. (See references 5 and 6 for perspectives about the situation in the more realistic case of asymptotically de Sitter spacetime, which is not understood as well yet.) In hindsight, Georgi/Distler's statement
...there’s no decoupling regime in which quantum “pure gravity” effects are important, while other particle interactions can be neglected
seems to be true in an even stronger sense in string theory. Here's an excerpt from section 2.2 in reference 7:
Typically, the mass scale associated to [quantum gravity] physics is [the Planck mass] $M_p$, and one might expect that working at energy scales far below the Planck mass would mean that we lose sensitivity to such physics. But the conjecture says that if in the bulk of moduli space... the tower of states has a mass scale around the Planck mass $M_p$ ..., then at large field expectation values this mass scale is exponentially lower than $M_p$. Therefore, it claims that the naive application of decoupling in effective quantum field theory breaks down at an exponentially lower energy scale than expected whenever a field develops a large expectation value.
Whether this "stringy" phenomenon is our enemy or our friend, it at least corroborates the idea that the interesting questions about quantum gravity are not things we can study properly by decoupling it from everything else.
Donoghue (1995), Introduction to the Effective Field Theory Description of Gravity (https://arxiv.org/abs/gr-qc/9512024)
Bekenstein (1973), Black holes and entropy, Physical Review D 7, 2333-2346
Hawking (1975), Particle creation by black holes (https://projecteuclid.org/euclid.cmp/1103899181)
Hawking (1976), Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460–2473
Witten (2001), Quantum Gravity In De Sitter Space (https://arxiv.org/abs/hep-th/0106109)
Banks (2010), Supersymmetry Breaking and the Cosmological Constant (https://arxiv.org/abs/1402.0828)
Palti (2019), The Swampland: Introduction and Review (https://arxiv.org/abs/1903.06239)
Best Answer
We don't expect quantum gravity effects to become observable until we approach the Planck energy, so the effective field theories for quantum gravity work at energies where they don't predict anything observable, and they don't work at energies where the effects would be observable. This is a strange way to define a reliable theory.
You are quite correct that the Standard Model is also (probably) an effective field theory, but it does make predictions in regimes where we can make experimental observations. This is the big difference from quantum gravity.