Psionic Potential is not inheritable, according to older material.
Correct.
The factors that lead an individual to have Potential are not known to Imperials, at least, and there are no indications except for the stated Zhodani social numbers to infer that the Zhodani have figured it out.
Actually, AM4 makes it quite clear that psionic potential is spread randomly among the
Zhodani population as well.
Noble status is inherited, but Noble position is not, since all positions above the baseline are elected.
Well, yes, but these are simply two different things, similar to what they were in most of early modern Europe. Whether you're a duke or an earl doesn't say whether you're a junior or a senior councilman.
The TU as a whole sees Psionic Potential in only a small percentage of the populace.
There is no reason whatsoever to assume this. Quite the contrary, it rather appears that all humans have
some psionic potential.
The idea that all Noble children are psions is either an artifact of PC generation or an indicator that the Zhodani are indeed different from Imperials when it comes to Potential.
Only if you assume that many humans have no psionic potential whatsoever. There is not the slightest reason in CT canon to assume this is the case.
so either that changed when I wasn't looking or the Consulate has a considerable population of non-Psion Nobles and Intendants who retain their positions through inertia.
Neither is the case. You base your conclusions on your (unfounded) assumption that some or indeed most humans have
no psionic potential. Since all of CT canon supports the opposite assumption, namely that all humans do have at least minimal psionic potential, there are no non-psionic Zhodani nobles or intendants.
I don't know how post-MT editions handled this, because I never bothered to check their psionics rules. But in CT and MT, operating with the information we have, there is no reason to assume the existence of non-psionic nobles or intendants in Zhodani society. There are going to be
weak-psionic nobles and intendants.
I think the misconception here is one of a "born" or even "racial" elite of psions ruling over non-psions. But the Zhodani system rather appears - and quite reasonably so, given its history - as a historically evolved ruling class monopolizing a certain "technology", in this case psionics. It is not defined by psionics. It uses psionics consciously as a measure of distinction (and an important aid in governing practice, although this only applies to telepathy.) Similarly to how ruling classes in Earth history monopolized certain types of military trainng.