Outdoor ranges don't usually allow it either, nor drawing from the holster...all liability.
I am not comfortable with 'running' and gunning. Walking quickly is another matter all together, however. We do approaches, retreats, sideways, and diagonals (forward and backward). We also do moves from station to station while keeping the pistol trained on target, shooting if necessary.
If you actually mean true running, there are a couple of control issues with which to contend. Human running involves a substantial bounce that is something like that of a gallop of a horse. Arms are likely necessary to maintain gait, hence aiming and shooting are extremely difficult, not to mention contending with the bounce as well. Full sprinting eliminates much of the elevational aspect of the bounce, but both arms are needed for the pump action at that speed.
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