This whole things real dumb.
I play a lot of Civ, player skill is what matters. Cops aren't OP. That being said, lets cover what you discussed:
Checkpoints: A Fun, yet invalid way to control the crime throughout the country. When cops sit in CPs, theres usually little to no volume for extended periods of time, thus essentially just being a time wasting simulator. CPs are fun in short bursts, with a lot of players online - Past that, They're not worth the stringent requirements that we've placed on them (That can't be lowered).
Air Patrols: Having Air Patrol is something the APD enjoys having, and is a perk to having superior officers online. If you want to be repeatedly caught by Deps who make errors on the regular, thats your perogative I suppose - but when I fight the cops, I want the chance to Shrek some Corporals+ and steal those helis from them. Also regarding this - there are very few corporals on the APD when compared to other ranks, if there is a heli on your server - you should be considering yourself fortunate that you dont have to ignore (Half?) of the possible combat situations that you get to deal with in Altis.