Since re-election is the key, term limits are effective only in so far as they get rid of re-election. If the limit is three terms, then two of those three terms will be spent trying to get re-elected -- and the third term will be spent trying to get elected to some other office.
What term limits need to do is make it nearly impossible to spend a whole career in politics. One term per office and some period of years outside of politics before running again would be a good principle.
Many people today marvel when looking back at the leaders who created the United States of America. Most of the founders of this country had day jobs for years. They were not career politicians.
George Washington, who took pride in his self-control, lost his temper completely when someone told him that a decision he was going to make could cost him re-election as President. He blew up at the suggestion that he wanted to be President, rather than serving as a duty when he would rather be back home.
Power is such a dangerous thing that ideally it should be wielded by people who don't want to use power, who would rather be doing something else, but who are willing to serve a certain number of years as a one-time duty, preferably at the end of a career doing something else.
What about all the experience we would lose? Most of that is experience in creating appearances, posturing, rhetoric, and spin -- in a word, deception. We need leaders with experience in the real world, not experience in the phony world of politics.