The assumption ignores that incumbency is the biggest advantage any lawmaker can have.
It’s much harder to keep trotting out a line of absolutely awful lawmakers into general elections without the benefit of incumbency than it is to trot out one absolutely awful lawmaker who managed to get elected once.
And a lot of the really awful lawmakers became that way over time rather than on day 1. There would certainly be no shortage of really awful lawmakers elected regardless, but a constant cycling of new faces would prevent the slower-creeping corruption from getting as bad.
The other thing that needs to come along with term limits is abolition of permanent benefits (like pensions) for elected officials. Boost up the yearly salary if necessary, so that actually serving doesn’t present a hardship to those with the desire to serve, but let the benefits stay in DC rather than following ex-elected officials home.
Politics shouldn’t be a career, and no one should be seeking election just to get a job with a ton of power and influence that will also set you up for a comfortable retirement whenever you choose to retire. It should be a sacrifice for a greater good, and people clearly can’t be trusted to run for office for the right reasons without rules to force it. Which sucks.