Congratulations on finding a method for baryogenesis that works! Indeed, it's true that if you have a bunch of black holes, then by random chance you'll get an imbalance. And this imbalance will remain even after the black holes evaporate, because the result of the evaporation doesn't depend on the overall baryon number that went into the black hole.
Black holes can break conservation laws like that. The only conservation laws they can't break are the ones where you can measure the conserved quantity from outside. For example, charge is still conserved because you can keep track of the charge of the black hole by measuring its electric field. In the Standard Model, baryon number has no such associated field.
Also, you need to assume that enough black holes form to make your mechanism work. In the standard models, this doesn't happen, despite the high temperatures. If you start with a standard Big Bang, the universe expands too fast for black holes to form.
However, in physics, finding a mechanism that solves a problem isn't the end -- it's the beginning. We aren't all sitting around scratching our heads for any mechanism to achieve baryogenesis. There are actually at least ten known, conceptually distinct ways to do it (including yours), fleshed out in hundreds of concrete models. The problem is that all of them require speculative new physics, additions to the core models that we have already experimentally verified. Nobody can declare that a specific one of these models is true, in the absence of any independent evidence.
It's kind of like we're all sitting around trying to find the six-digit password for a safe. If you walk by and say "well, obviously it could be 927583", without any further evidence, that's technically true. But you have not cracked the safe. The problem of baryogenesis isn't analogous to coming up with any six-digit number, that's easy. The problem is that we don't know which one is relevant, which mechanism actually exists in our universe.
What physicists investigating these questions actually do involves trying to link these models to things we can measure, or coming up with simple models that explain multiple puzzles at once. For example, one way to test a model with primordial black holes is to compute the amount heavy enough to live until the present day, in which case you can go looking for them. Or, if they were created by some new physics, you could look for that new physics. Yet another strand is to note that if enough primordial black holes still are around today, they could be the dark matter, so you could try to get both baryogenesis and dark matter right simultaneously. All of this involves a lot of reading, math, and simulation.
In Figure 24.1 of https://pdg.lbl.gov/2020/reviews/rpp2020-rev-bbang-nucleosynthesis.pdf they plot light element abundances as functions of baryon-to-photon ratio, according to theoretical prediction. The CMB value is vertical narrow line which is centered at around $6\times 10^{-10}$ (they use logarithmic scale). Yellow boxes are from observed light element abundances. The lithium abundance is in tension with other light element observations as well as CMB data, so they refer to it as "lithium problem".
In https://arxiv.org/abs/2106.05338 they used different baryon asymmetry parameter (baryon-to-entropy density) which I already mentioned here.
The baryon density, $\Omega_bh^2\approx 0.022$ ($h$ is a conventional normalisation parameter -- essentially dimensionless Hubble parameter), used in the Planck paper is again a different parameter. This is baryon density fraction with respect to total energy density of the Universe (which is close to one).
Best Answer
To achieve a nonzero baryon asymmetry, one needs to satisfy the so-called Sakharov conditions:
If at least one of these "asymmetries" or "imbalances" is missing, the total $B$ of the Universe will remain zero.
The Standard Model preserves $B$ perturbatively (the baryon number is an accidental symmetry preserved by the renormalizable interactions), so it violates the first condition. In fact, while it violates C and CP, the violation of CP via the CKM matrix is too weak so even the second condition fails. The typical processes described by the Standard Model tend to be close to thermal equilibrium as well but the failure of one condition is enough so we don't need to be too specific about the last claim I made. The conclusion is clear: One needs models beyond the Standard Model to create a baryon asymmetry. This much has been known for decades.
However, the Standard Model contains some kind of generalized instantons, the sphalerons, that may convert the lepton number $L$ to $B$ and vice versa. So the first condition, $B$ violation, may be replaced by a combination of SM sphalerons and $L$ violation.
That's why the models producing the baryon asymmetry may be either the traditional "baryogenesis" in which the baryon number is clearly violated, or "leptogenesis" in which the lepton number is violated and the lepton asymmetry is later converted to a baryon asymmetry as well. One may discuss various thermal and non-thermal versions of these processes within various theories beyond the Standard Model such as the grand unified theories. The grand unified theories are rather characteristic for the literature because the characteristic scale of the physical phenomena responsible for leptogenesis or baryogenesis is usually assumed to be close to the GUT scale, up to 15 orders of magnitude above the LHC energies.
The literature on leptogenesis and baryogenesis is comparably large. For example, both words appear 700+ times in the titles, see
I invite you to check some of these papers. There's of course no universally acceptable, unambiguously superior model of leptogenesis or baryogenesis at this moment because there's also no clearly preferred model beyond the Standard Model. Physicists just don't know what the right mechanism producing the baryon asymmetry is. However, the field is sufficiently advanced that newly proposed models of beyond-the-Standard-Model physics are routinely tested on whether or not they provide us with a viable mechanism for baryogenesis or leptogenesis.
A viable form of leptogenesis or baryogenesis is usually demanded together with a realistic enough implementation of cosmic inflation and with other cosmological constraints associated with high enough energy scales (e.g. the absence of the moduli problem etc.).