You’d also have no accountability after being elected, since they wouldn’t face the voters again), and in the odd chance that you got yourself a good Senator you’d have to give him up and face a crapshoot every six years. And with new Senators coming in every six years, unelected Senate staffers would wield even more power. Besides, I’m not too sure about a single-term limit relieving them of pressure to fundraise, since many of them would be fundraising for some other office (that’s certainly been the effect of term limits in state legislatures).
VA has a single-term limit for governors, and I don’t think that it’s led to better governors than in states without term limits or with a limit of two terms.
We don’t need term limits, we need better educated voters.
Of course, there’s hardly that much accountability now. They do what they please for 5 years and only pay attention to the voters for part of the election year.
I’m also aware of the powerful, behind the scenes staffers, and something will have to be done about that as well.