The thing about a TNG phasers having 16 settings was going with Roddenberry's idea that it was as much a tool as it was a weapon. Anything above Setting 8 was for blasting through solid rock or other dense materials, with the higher settings allowing for greater rock displacement up to a few tons, IIRC. At that point, a phaser was more of an excavation tool than a weapon.
Generally, I think most phasers rarely went beyond Setting 8 as anything higher would be overkill in normal circumstances like you said, but higher settings are nice to have if you find yourself trapped in a classic Doctor Who quarry or something like that...
Free your mind, and the rest will follow.