I have done less than full power takeoffs many times, for varying reasons. In my flying boat I found to my surprise, that with some careful handling, I can takeoff, fly, slow to descend from within ground effect (water really), land, and takeoff again, all at 19" MP, without touching the power. Doing that is just a skills thing. Other takeoffs are partial power just to be nice to neighbors, particularly on lakes, both wet and frozen. Flying single pilot turbine, I have done partial power takeoffs to prevent having to very carefully set power during the roll in a tight runway. There's always more power if I push the power lever, so if partial power is trouble and worry free for over temp/torque, so much the better. Better eyes out on the road! Last, and fearsome, there are some higher performance single taildraggers, which are going left off the runway, if you open up the power at an airspeed below that in which the rudder has effect. Partial power until the rudder rudders!