I come from the Gliding community with a limited experience of power (mainly SLMG). We always teach elevator for speed, brakes for rate of descent as has already been described. A "problem" we have with new students in the early stages of teaching approach and landing is that they want to aim with the elevator and control speed with brakes (similar to your point/power question). This raises a couple of issues in our aircraft types. Firstly, if the approach is started too high/close, the brakes cannot reduce the speed sufficiently and 5-10kts excess speed in something as slick as high performance glider results in a massive overshoot-bad news in a short field landing. The other "gotcha" of this method is a long/low approach where the risk is that the glide is stretched with no brake resulting in, at best an under shoot or decaying airspeed and a stall/spin .
A final consideration is that whilst some gliders are flapped a great many are not, therefore when the brakes are opened they spoil the lift and create drag but give no increase in lift, resulting in an increase in ROD (steeper glide path) and elevator used only to maintain approach speed. Whilst it can be argued then that the elevator contributes to the increased rate of descent, with small brake settings the affect on airspeed can be almost negligible. This is most readily seen in low level launch failures where cracking the brakes open will risk slamming the glider into the ground whilst still having flying speed.
As for landing fast, landing on is a no-no, with a fully held off landing and the stick on the back stop required, in which case the touchdown spot will inevitably be further up the runway.
I would say that most tug pilots I know use elevator for speed and power for ROD but then most I know glide in on idle, with a dead stick style approach,
Ian