Several things pop up in my mind immediately - the most obvious is, more experience in politics is very often thought of as a bad thing. If a political system has become stagnant or even has resulted in the decay of a national infrastructure, the systems therein, people typically recognize that corruption and laziness and capture from powerful often scary outside systems and people are the cause, and any politician that’s been participating the entire time is more likely to be complicit compared to a new comer. At least that’s the pervasive belief of the general populace.

Two - often higher numbers of degrees or accreditation just means harder work ethic, but not necessarily better innovation or the novel capabilities and insights needed to meet the moment for the right change necessary. A great example is Lincoln, who is hailed as one of if not the greatest President for many reasons, but most notably saving the union from fraction and self destruction. He was known as a self taught great orator, extremely intelligent but only had 10-12 months of formal education total. His entire life. Very often innovation and genius comes from unexpected places, and cutting that out as a potential source for solutions and leadership would be a very serious mistake.

Three - limitation based on achievements marked by what’s been seen by some as an elite, inaccessible to many system that is flawed in how it teaches and tests its candidates serves to keep power, access, top roles from demographics historically, a great example is how voting during the heights of racism in the US requires literacy tests to ensure minorities couldn’t vote because it was illegal for minorities to go to school and learn how to read. This applied in other ways to women as well. The same can be applied to people who can’t afford a masters or phd, or even to finish high school because they have to work to help their family survive. A higher degrees example might be how Harvard and a few other ivory league universities hold the vast majority of some occupational positions, 16 of the Presidents being one example.

It’s worth noting that 12 presidents had no degree, including Washington, so we wouldn’t have had those people or their leadership. That might be good in your opinion, but the world is different now and applying limiting tests like that today would severely limit the pool from which we could select candidates, and most people don’t want the job tp begin with, which limits it to very few, many of which you really don’t want holding that power.