One of the problems is that some of these checks can only be performed much later.
The most common currency of choice, for modern bribes, is the promise of a fat gig in the private sector when the political career ends. As the public demands younger and younger political classes, with lower and lower salaries, while maintaining an appetite for career-ending scandals and relatively short terms in office, it's inevitable that individuals will tend towards ensuring their future survival. Such promises need no paper trail, are trivial to keep, and are effectively invisible for years. When they're realized, it's typically too late to do anything about the original source of corruption, and the new guys in power have no incentive to cut that income source for them; in fact, they now know it works and are more likely to tap it for themselves.
Looking into the US senate, I fail to see that trend. In the last presidential election, both candidates were older than my grandparents.
Even in my country, seeing a really young person in a political position is very rare. They exist (if you define "young" as under 40), but they are rare. I don't think age worries are a factor at all.
Look at the pay for members of the House and Senate, in real dollars, over the last 50 years. Also pay attention to how much stupid noise there is about how members of Congress are supposedly overpaid. The pay for all US Senators combined (under $18M) is less than half of what LeBron James makes (over $41M) in salary alone in a year.
> They exist (if you define "young" as under 40)
In political terms, at the (European) national level, "young" is typically under 50, and "old" is over 70. Acquiring reputation and solid power base takes time.
Looking at the UK: Tony Blair was considered very young when he became PM at 44; Thatcher was 53, Major 57, Brown 56, and most of their predecessors were much older. Cameron was 43 but again May was 59 and Johnson 55. Backbenchers will typically enter Parliament around 35-40.
In Italy you can basically add 10 to all those numbers; the current PM (or PdCM, for the purists) is 73.
But then would has the potential of misdirection. Your believed set of would's might be entirely separate from the realized would's of the individual. Could is wider but has less room for interpretation or propagandizing. Exactly my point in the above post: why wouldn't they be able to transfer money. My set of would's include those deliberate obvious actions, especially if all kinds of other things happen on golf courses. Anyways, I'm rambling, have a nice day. :)