I've been working on golf courses since 1993. Every place I have been mows their collars/tees at different height than the fairway. Usually collars/tees are same height for some of the reasons stated above.
I think mowing collars/approaches a little tighter allows a better opportunity to put and bump/run a shot and now one wants a long collar next to a green being mowed under 1/10"
A must reason for mowing at different heights is as I stated above-different turf. When we maintained tifeagle approaches/collars & tees at Pine Tree, we never cut above .200" because, well...it never really grew any higher. Fairways were maintenance at .400-.550" depending on time of year.
We have paspalum tees here, so they are mowed with a walkers that do not mow any other turf type, so it's easy to adjust heights and not effect anything else.
I think fairway height, has to be higher because fairways are generally are not maintain as intensely as collars & tees. Fairways are being driven on by carts & larger machines, most are not handwatered, therefore a higher height of cut reduces stress.