Might want to look at how that has worked at the state level. The state of Michigan has this and it has only exacerbated issues held in check because people had incentives to help people and get re-elected. Michigan now squarely gets its policies from lobbyists and special interest groups because at the end of their terms that is who will hire them.

Term limits do exist and are called elections. Every single election is a chance to vote someone out of office who hasn't done a good job. The thing that has essentially broken elections as term limits is partisan gerrymandering.