I think the Colleges produce reliable, dutiful, and loyal people because that's literally what they're designed to do. And part of that is by placing the "responsibility" over "opportunity" in every teaching and rule and value.
The Colleges could produce more powerful wizards in greater numbers if it was willing to compromise on how highly it values loyalty, reliability, responsibility, and duty. It does not, because the Colleges view the responsible use of magic as far more important than the powerful use of magic.
We see this in the mentality of basically every College wizard we come across. Their personal ambitions either align with or do not conflict with their responsibilities, duties, and rules/laws. In any edge cases, they take significant measures to smooth over potential conflicts--Gretel enjoys a much more materially wealthy lifestyle than Amethyst wizards normally do because she works in service of the Karaz Ankor (whom are famous for being trustworthy, honorable, and reliable) well outside the Empire's borders (and thus doesn't risk tarnishing the reputation of the Amethyst Order), and can justify it as a useful method to impress the people of the Border Princes through peaceful means rather than force or magic.
Mathilde is way more wealthy than you'd expect from a Grey Wizard under the Vow of Poverty, but she balances it by putting that wealth to use for the benefit of the Empire in tangible ways related to her duties, combined with a VERY active career in service to the Empire and its allies such that it's easy to argue that she doesn't have time to try any funny business. The main vehicle for her wealth, the EIC, is very obviously a staunch supporter of Stirland and its very important efforts to pacify and secure Sylvania and the Karaz Ankor's efforts to support Karak Eight Peaks and other karaks in the region.
The leader of the most wealthy of the Colleges personally led and coordinated the efforts of the Battle Wizards in a campaign against the vampires of Sylvania, and every effort we've seen from them has made them look like a research and scientific institution with magic than some wealthy juggernaut bringing the Empire under its thumb through money.
Every opportunity that comes from being a wizard of the Colleges also comes with equally heavy (or even heavier) responsibilities and duties, not to mention risks.
It will definitely be interesting to see how Manfred's life unfolds. How will the Colleges approach a situation in which an Elector Count-to-be will also become a wizard? My guess is that they'll have to find a path that involves teaching the values of the Colleges without denying the responsibilities and opportunities of such high-level leadership, but also making sure not to even appear like they're treating it like an opportunity to exert influence over Reikland using Mandred.
Yeah, the Colleges have a pretty story. So does the Imperial aristocracy. In many ways, it's the same story. There's a special group of people, who are raised in an environment that provides them with extraordinary skills and teaches them about responsibility and duty. These "best ones" are clearly wiser and more virtuous than ordinary people.
Remember the Night of a Thousand Arcane Duels? That time when the Colleges decided to have a giant battle royale in the middle of Altdorf? Apparently all of that wisdom and virtue was taking a vacation.
Reliable, dutiful, loyal. Are we talking about Alric here? The man who was and might yet again be the head of the Light Order? Yes, he is clearly a perfect example of a leader who places the needs of the Empire above his own personal ambition. It's a good thing he was brought up in the Colleges. Without that education, he might be an ambitious bastard who uses his apprentices to advance his own career.
Don't get me wrong, there are wizards who believe that with great power comes great responsibility. They may even be a majority. But wizards are
people, and people are often selfish bastards. We're also fond of finding elaborate justifications for being selfish bastards.
I'm sure that during the Time of the Three Emperors, all of the different claimants had stories about how they were reliable, dutiful, loyal children of the Empire. They told themselves that it was their
rivals who were the self-serving warlords, while they were only acting out of sad necessity. Somewhat like the Colleges, when they were burning down Altdorf.
Mathilde doesn't really go into it, but the Night of a Thousand Arcane Duels reflects very badly on the Colleges. They clearly had some serious rivalries buried beneath the surface, and when those rivalries came out most of them didn't give a damn about what might happen to the little people who got caught in the middle.
If you ignore the Night, and you ignore the existence of Black Magisters, and you ignore any wizards (Alric) who contradict the pretty story, then it's a
great story. Propaganda is often simple and lovely, while reality is unpleasant and complicated.
Of course the Colleges want to exert influence over Reikland! Of course they're going to use Mandred to pursue their own agenda! This isn't even bad, it's just politicians advancing the interests of their constituents. But we shouldn't pretend that the Colleges are some noble paragons of virtue, like Magnus the Pious come again. They're playing the game, just like everyone else.
The Grey College is an organization of paranoid, secretive schemers who take pride in doing whatever the hell they want. Both Regimand and Mathilde have murdered
royalty without the benefit of trial. In Mathilde's case, Vladimir wasn't involved with any vampire or Chaos conspiracies. She just didn't think he was good at his job, so she killed him.
You could certainly say that murdering a friendly head of state with magic is not a responsible use of magic. However, the Grey College's motto is not "Do the right thing". Their motto is "Don't get caught". For all we know, there are any number of Grey Magisters who horribly abuse their power, but they're either good at covering it up, or the College finds out, murders them, and then covers it up.
