Why not always take off with 10 degree flaps in a Cessna 172?
Flaps out will reduce the ground run, but you're forgetting that they also increase drag. This is why you don't climb all the way to cruise altitude with flap extended. A 172 will climb better without flaps.
With a take-off, you have to consider both the ground run and initial climb. After all, the take-off distance required is defined as the distance required to climb to screen height (50ft in Australia, sorry if the US is different). The aircraft also has to meet a legal minimum climb gradient to that height.
Without looking at the data, it is possible that in certain conditions, taking off with flaps 10 will get you off the ground quicker, but will actually take longer to reach 50ft compared to a takeoff with no flaps. In any case, retracting flaps in a busy time after takeoff is a potential hazard, and in a training aircraft like the 172 simple procedures are best.