The automated selection of reduced climb thrust on the 737 will take assumed temperature into account, however it is user selectable to a higher climb thrust and that is what we do based on input by Boeing and CFM. That will lead to increased thrust at thrust reduction altitude in nearly all cases.
The lowest usable flap setting on the 737 is 1 and that is indeed the most often used one, however especially during winter the higher take off flap settings up to 25 are routinely used as well, depending on runway condition and obstacle situation.
Well, today that gizmo is realized in software, but it is still in use and can actually lead to reduced leasing rates and of course maintenance costs. It isn't shown to the flight crew though. And engine abuse is reduced a lot since FADEC takes care of keeping stuff within limits most of the time.