Term limits make it vastly easier for politicians to be captured by special interests. Politicians lose "doing a good job" as a way to have a continued job going forward, making them more susceptible to looking at how their vote will impact their future employment. It also means that even well intentioned representatives don't have time to properly learn how the system works and become effective before they need to leave, making power shift to unelected groups. At best their political party providing knowledgeable staff and legislation to propose, and as is often the case various special interest groups who can work to finance campaigns as well as provide pre-packaged legislation, media campaigns to encourage voters to encourage you to pass it, and assurances of various roles that can provide post political life influence and money.
The way you reduce the influence of interests is to make it so their levers don't work anymore. If politicians get a pension even after being voted out of office a cushy board position is less appealing. If they get paid generously in office there's less incentive to court outside influence, or risk your money by accepting it. If you can keep that going as long as voters like you, you only have incentive to keep voters happy.
Finally, why would you want to say to voters "sorry, this politician consistently provides what you're looking for in a representative so you can't have them anymore. You need to pick someone new who doesn't have any legislative record or experience"?