.if hairless armpits are easier to clean then surely we should all shave our heads
Completely agree with seren nos.
I've never found hairy armpits hard to clean. A bit of soap and water seems to do the trick wonderfully quickly and with very little effort (And I've never found "debris" in there like I think someone else mentioned.) 
Shaving armpits is fine if that is what you prefer to do but I really can't see that it has anything to do with hygiene.