What you're proposing would be swiftly corrupted by the people in power deciding what qualifies as "educated enough" or "security clearance".
Accept anyone from Jebus University with its miraculous 100% graduation rate, exclude anyone with a record of "Disrespecting an Officer", and the pool is quickly skewed, a reinforcing feedback-loop in favor of the groups doing the skewing.
True, you cannot start sortition as a good means of re-distributing power in an already centralized system.
It is a method to help maintain a balanced distributon of power, not created it when already gone awry.
In democracies, the branches of govt, legislative, executive, & judicial, and the institutions of society including the press, academia, industry, finance, sport, religion, etc. are all independent and serve to distribute and balance power. In autocracies, all of those are corrupted and/or coerced to serve the whims of the executive.
So, of course, an already-powerful centralized executive would be able to corrupt it as you describe.
But it seems much more difficult to make it happen in a well-balanced system, particularly when some have the responsibility to ensure ongoing fairness.
Do you have a better solution?