Now, the idea of electing a few thousand representatives and having sortition determine who is actually selected is something I could feasibly get behind.
Not selecting absolute random people, but people who have established their ability to intelligently handle responsibility, and avoid breaking the law. E.g., once you have achieved a certain level of educational attainment (3.0+ at well-ranked college, managerial-level at established biz, certain mil leadership rank, etc.), pass security clearance, pass citizenship test, etc., you are in the qualified pool, and may be called upon to serve in a legislature. The always-a-newbie problem could be solved by allowing legislators to serve 2nd or maybe 3rd terms by re-election/confidence vote. Same for POTUS, possibly selected by sortition out of the existing legislators who pass a confidence vote.
There is no way a reasonably and responsibly selected random group of achieving responsible people would do worse than a corrupt or craven group, especially worse than the selected-for-corruption — i.e., selected for loyalty-to-leader — currently seated.
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.
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?