Why aren't large, low-speed propellers widely used?
You are not wrong, it is more efficient to accelerate a large mass by a little than a small mass by a lot.

This is due to momentum being linear with speed and mass, while energy is linear with mass but quadratic with speed, so the same momentum can be obtained more efficiently by slowly pushing a large amount of air, e.g. with a large propeller.

The reasons against this are as you imagined, like clearance from the ground and other parked craft. Also, extremely long propeller blades will suffer from high inertia and bending moments, without the benefit of centrifugal stiffness. And then there is the issue of keeping the propeller tips subsonic, to avoid wasting a lot of energy in the form of sound.