My observation is it is the hours that kill an APU, not the thermal start/stop cycles
Wrong! It is definately thermal shock during start cycles that kills apu's. I know of a pacific island a/c that left its apu running from when the a/c was first started in the morning till when it was shut down at the end of the flying day (mostly because of the remoteness and likely hood of problems if it didn't start) and when it was removed due to hours and disected in the workshop it was in absolutely pristine condiction. With regards to apu starter wear - starter motor brushes are easily replaced. New gen 737's actually have a starter/generator these days.