I think I remember that discussion. I will restate my position that I would in fact rather see it as "wizards with nobility" rather than "nobles with magic powers". Being a wizard inherently changes how others see you in a way that nobility really doesn't. And nobility is not something so utterly ingrained that that the Colleges' training for Apprentices cannot overcome it and hammer in the fact that a legal wizard's first loyalty is to the Empire as a whole.
While I do think you're making a great point regarding how a lot of common folk or burghers wouldn't really like to be ruled by people with powers they can't understand or even see, I think the better questions to ask are:
"Would most nobles even want magic, when a good number of people think of it as a curse and inherently fear magic? How many of them would instead decide to have their potential sealed away?" "Would most nobles want to use Ulgu, when the Grey College is known to be super strict regarding the usage of its powers and to not use it for personal enrichment?" "Would many existing magic families even want to rule, when they probably already have their own personal bugbears and projects to deal with, and being in charge is the sort of thing that takes up a lot of time?"
If you can do that, if training and culture can do that, can't you just do that for nobility to begin with in the first place?
And if magic is something that provides more opportunities to be good or bad; to be either trusted with power, or to fail and thus not be trusted with power, and thus is a better sorting mechanism or so the argument would go... well, everybody would have an opinion on the assertion of "Magic makes me better because I have more opportunities to be morally tested, and thus my kind should rule."
Other problems arise, too; wizards are policed by the Colleges... who are centralized in Altdorf. This would be rule-by-Altdorfian-culture/institutions. "the Colleges' training for Apprentices cannot overcome it and hammer in the fact that a legal wizard's first loyalty is to the Empire as a whole." would be creating not a new and more-improved strain of nobility, it would be forming the basis of rule by federalization or centralization. Which, well, your answer might be "But if they're the best(TM) anyway, what does it matter if they all go to Altdorf to get taught?" but, uh, everybody else would have an opinion on that. This wouldn't be seen as rule-by-Wizard-Nobles, this would be seen by at least some as an attempt by an institution (or 8 institutions) localized and centralized in Reikland to assert rulership over all the others.
Maybe you could test the system out in Reikland alone, and see if it has good or bad outcomes. But then, how would you export the system elsewhere? Would you form more Colleges of Magic in each province? And if so, would each College try to be a carbon-copy of the Altdorfian institution and mores, or would it try to be one that asborbed and exemplified the more and values and religions and cultures of the locals?
Also, what if people don't want to be locked out of the highest stations of power simply because they lack magic? What if people wanted the possibility of rising to nobility -- or marrying into nobility and they or their non-magical children becoming nobles -- without having magic or their kids needing to have magic?
My thoughts were partly thinking from the perspective of "Assume that people with power are going to act like people with power; and look at this from a long-running or multi-generational outcome rather than just a 'What would the first generation be like?'" Which is why my answer was "Well, people with power will act like people with power do. Except this time they'll have more personal power at hand, to boot." Hence why I viewed it as "Nobility with magic" rather than "Wizards becoming nobles". Because in the long run, that's what it would become; nobility having to be trusted with magic power. Rule by wizards.
That "the first generation would be like" thing is also pretty important; because the people that carve an empire or a nation out of nothing, or from a crumbling empire or set of nations,
are not the same as the people that will replace them and will come later. Wizard Nobles might be fine
now, because of the standards or training of the Colleges, but
that might come down to a variety of factors one of which would be a sort of hybrid vigor or first mover effect.
Also, what if one of the reasons that the Colleges have good outcomes, is
because of the limitations on their powers and the strict responsibilities placed upon them? Or because they're only one part of the apparatus of the Empire, with other roles and parts being taken up by other peoples?
What about the wizards that
don't want to rule? What if the Amethysts/Ambers/several-others wind up mostly
not being the sort of personality that wants to rule, and it's, say, the Celestials that are far more happy to rule? Or worse; what if opening up nobility and rulership to wizards, means that every wizard who is an ambitious sort, now has a pathway or goal for that ambition; namely, to become a noble. Meaning that the more humble or easygoing wizards remain workers or servants or wandering heroes or soldiers. While the ambitious strive for power.
Basically "What if it's the limitations on their ambitions and positions, that are one of the reasons wizards are good and effective?" restated again; i.e. "If you open the doors to power and status, don't be surprised if you get power-striving and status-seeking people come running."
Hence why I stated it as "View it as 'nobles with magic power'", because that's what it might come down to over the generations. Open the ceiling for powerful and ambitious people to obtain status/wealth/power, then don't be surprised if you
get powerful and ambitious people seeking power and wealth and status. You will inevitably get this in any scenario involving money/power/fame. Hence why maybe wizards shouldn't rule, because maybe the best usage out of them, is in ways that focuses what their
magic can do for the Empire ((as guided by their integrity and character, which is molded by the wizard and the College)) rather than whether their integrity and character can make them good rulers. Because maybe if you take the wizard out of the current ecosystem he operates in, maybe things change a lot.
... And also, if wizards are busy ruling, then they're busy not being wizards. Is it a good thing to tap into our reserve of people-who-can-use-supernatural-powers for rulership, rather than utilizing them for whatever-position-supernatural-powers-are-best-used-for?
Is Mathilde or Panoramia or Max better placed as a ruler, or as somebody who creates Waystones or rehabilitates farmland or helps translate Queekish? And maybe the Mathildes and Panoramias can remain researchers and farmers and heroes; but if they disagreed with who was going to become a noble, they might feel compelled to take up power themselves, or to block others from having that power, and you wind up in the same question of "Was it really to make them a ruler rather than a researcher/hero/soldier/farmer/etc?"
At the least, it might mean that wizards have to care about politics and power even more than they already do. Which might get tiresome or undesirable for some wizards.