"which actually make the problem so much worse"

I'm sorry you haven't made that case at all. All you have done is listed the costs of the "term limits" side, you haven't listed any of the benefits. A couple off of the top of my head:

1. Seats would be up for effective election more often allowing for democracy to perhaps function more effectively. Perhaps there would be more of a market of ideas instead of cults of personality.

2. Less time for legislators to establish "ties" (corruption) with regulators, business leaders, party leaders, and others in power.