As a clarification the energy per nucleon is always lower: for example, currently in the LHC the proton top energy is 3.5 TeV. Now the Pb energy is 3.5 TeV times Z so the energy per nucleon is 3.5*Z/A and A is greater than Z for every nucleus (except the proton where it is equal to one).
But the goal of ion-ion collision is not to increase the total energy or the energy per nucleon: it is to obtain a different type of collision.
It should be noted than in a proton-proton collision, the energy involved in the real collision process is variable: each quark and gluon carry a fraction of the energy of the proton, and hard collision involve a collision between a quark/gluon of one proton against a quark/gluon of the other.
In the case of ion-ion collision you have the same process: the energy is shared by the protons/neutrons and they can have different energies.
The goal of such collision is also to obtain a volume (bigger than in a p-p collision) with a very high energy density. In such a volume, a "state of matter" called quark-gluon-plasma is believed to be possibly created. The study of this QGP is one of the main goal of the ALICE experiment at the LHC.
A few references:
A subtle problem you seem to overlook is that the proton-proton cross section is very small, about 0.07 barns (a barn is $10^{-28}$ square meters) at the LHC energies and not dramatically different at your lower "fusion energies". It means that at the LHC, much like at your dream machine, most of the protons simply don't hit their partners. It is not really possible to focus the proton beams arbitrarily accurately, for various reasons (the uncertainty principle is the truly unavoidable effect: you either localize the beams in the transverse direction, into a "thin pipe", or you specify that the velocity in this transverse direction is zero which is needed if you want to preserve the location "in the thin pipe" in the future, but you can't do both at the same moment). If it were possible, the LHC would be among the first ones that would use the method, to increase the luminosity.
So if you accelerate two beams of protons against each other, an overwhelming majority of them will simply continue in their original motion. (The protons in the LHC have to orbit for half an hour or so – tens of millions of revolutions – before one-half of them collides or disappears.) It costs some energy to accelerate the protons to these energies and you want this energy to be returned from fusion, with some bonus. But the fusion only returns you the energy from the protons that collided (some of them could create helium at your energies but there will always be nonzero probabilities of other final states; it's not a deterministic system that always produces the same final state for a given initial state; quantum mechanics says that the outcomes are random) which is a tiny portion of the protons. So you will be losing most of the energy you invested for the acceleration. Note that the LHC consumes as much energy as the households in Geneva combined and it just produces collisions of protons whose energy is smaller than a joule per pair.
To increase the fraction of the protons that hit their partners, you either need to send them to the collision course repeatedly, like at the LHC, but then you need to pump extra energy to the protons that they lose by the synchrotron radiation (which is always nonzero if the acceleration vector is nonzero, e.g. for all circular paths). Or you will need to dramatically increase the density of the beams.
But if there are many protons in the beam, they will electrically repel each other and you will become unable to focus them for collisions, too. So what you need to do is to electrically neutralize the high-density proton beam and then you have nothing else than the plasma and you face the usual tokamak problems how to stabilize it. Note that the electrons respond totally differently to the external electromagnetic fields than the protons. The LHC uses both electric and magnetic fields to accelerate the protons but to keep the plasma neutral, you must avoid electric fields.
Tokamaks only work with magnetic fields. Whether they will ever become fully working and feasible remains to be seen but the absence of the electric fields implies that they don't have much in common with particle accelerators.
Best Answer
The ultra high vacua in the present collider experiments are needed for two reasons
To make sure that the detectors are getting the debris of pure proton-proton hits, and not of random molecules ( which still exists because no vacuum is complete,and have to be included in a background for the Monte Carlo simulations of the interaction).
Keeping the beam intact , i.e not losing energy and direction through the scattering you describe, and becoming useless for accurate measurements.
In the early times when one was studying interactions of particles in bubble chambers and detectors , the beams were crerated in vaccuum, but arrived at the detectors through air, at least in bubble chambers I am sure it is so, because I worked on Kaon experiments at CERN. That is because the incoming particles were seen one by one parallel, any interactions would take them out of the beam and they were not so many because the intensity of the beam was kept so that a small number of particles arrived at the detector.
If we lost the beam we used to joke that "a cat had entered the beam line".
For more intense beams used in electronic detectors the air beam would be dangerous, even if not intense enough to be visible.
Edit after finding this reference, page 343:
The photo is in order to show how the beam interacted with the scintilators, no light is seen in the air .The hall was well lighted all times, the photo could not have been taken with the hall lightings on.
So the physicist must have been checking a beam line, thinking the synchrotron was off, but it either was still on, or it came on without alarms going off.