Is it an overkill to request to see airplane maintenance logs at a new flight school?
I'd refer to FAR 91.3(a):


  The pilot in command of an aircraft is directly responsible for and is the final authority as to the operation of that aircraft.


Therefore, I believe you have a duty to determine that the aircraft is properly maintained.   While that doesn't mean disassembling it and checking the work yourself, I do think that its reasonable to verify that the maintenance logs have recent entries, and appear orderly.

At my old flight school, I never got any grief at all (and occasional complements) when I wanted to see the logs for some reason.

If they give you so much as an eye-roll when you ask to see the logs, that should be a cautionary sign.

I think it is also an easy way to meet the maintenance guys, and be introduced to them as a careful, thoughtful pilot.  (The Mx guys likely despise "cowboy" pilots who bring back damaged equipment, and don't report it.)  You'll get to know some people at the new school, and get a reputation right off the bat.