Term limits do nothing except increase the probability of having bad/corrupt representation.
I suggest that we give them a try before making statements like that as if they're facts. Congress (that would be both the Senate and House) have never had term limits since the Constitution was created. I would counter your suggestion by claiming that term limits would help combat the type of de-facto oligarchy that we see today.
Think politics has gone downhill over the last 30 years? That's about how long it's been since term-limits started getting popular.
Thomas Jefferson of Virgina wrote in 1789 that he saw term limits as necessary "to prevent every danger which might arise to American freedom by continuing too long in office the members of the Continental Congress". That wasn't the first time they were discussed, either. Back when states were ratifying the Constitution in 1787-88 statesmen like Richard Henry Lee viewed the absence of term limits (as well as other perceived shortcomings of the Constitution) to be "most highly and dangerously oligarchic". The Bill Of Rights was created to address the issues that many states had with the Constitution, although term limits didn't make it in. In arguing Jefferson's side, George Mason said about Presidential and Senatorial term limits, "nothing is so essential to the preservation of a Republican government as a periodic rotation". Female historian Mercy Otis Warren, born 1728, said "there is no provision for a rotation, nor anything to prevent the perpetuity of office in the same hands for life; which by a little well-timed bribery, will probably be done". There was also discussion during the 19th century, and also the 20th, but nothing got done primarily because the people who would be hurt by term limits are also the people who need to make them law. At this point it seems like it would require an Article V convention of the states to circumvent Congress and implement term limits as a constitutional amendment.
But, instead of your suggestions about what may or may happen with Congressional term limits, and considering the fact that we have never had them and that Congress appears to not be working for the people, I would suggest that we try them and see what happens after a few decades.