Term limits stop 2 things, career shitty politicians and career good politicians. People realize that they can't do their own surgery or program their own computers but spew out the old "any old guy off the street can be a politician" like it's on sale without ever bothering to recognize or admitting the fact it's a skilled trade just like a surgeon or a software developer and one tends to increase their skill at it with more experience. What people who make statements like the above want but can't manage to actually say is, "no shitty career politicians" but that belies the fact that humans are incapable of selecting politicians for candidacy that are anything but unwavering partisans without any intention or ability to do what politics is meant to do, resolve contradictory mandates to achieve a rational mean where neither side gets what they want but both can tolerate what they do get. The problem isn't the politicians, it's the people. An example from literature which is very much appropriate (credit - Douglas Adams, HHGG):TERM LIMITS, WILL STOP CAREER POLITICIANS.
“[Ford said] ".. On its world, the people are people. The leaders are lizards. The people hate the lizards and the lizards rule the people."
"Odd," said Arthur. "I thought you said it was a democracy."
"I did," said Ford. "It is."
"So," said Arthur, hoping he wasn't sounding ridiculously obtuse, "why don't the people get rid of the lizards?"
"It honestly doesn't occur to them," said Ford. "They've all got the vote, so they all pretty much assume that the government they voted in more or less approximates to the government they want."
"You mean they actually vote for the lizards?"
"Oh yes," said Ford with a shrug, "of course."
"But," said Arthur, going in for the big one again, "why?"
"Because if they didn't vote for a lizard," said Ford, "the wrong lizard might get in.”