I'm not sure any problems would be fixed. The way things are now, politicians in the house/senate have to always worry about re-election, and at least create visibility of catering to their electoral base in the run-up to that. If their second term did not have the possibility of re-election, they'd just do what the lobbyists want them to 100% of the time (as opposed to 90%) in exchange for a job after their second term ends.