Apologies if this is going to bore some people ...
A high shot can go just as far as a low shot. Gravity is essentially insignificant in terms of shot distance.
Somebody please step-in if what I am about to say is complete garbage ... i.e. sombody who could share their calculations ...
Hydrodynamic attenuation of kinetic energy is more important ... i.e.
roughly the same for high and low shots.
(Ground-effect comes into play for low shots)
On average ...high shots go farther than low shots
Why ? ... because they effectively travel a maximum potential distance before their energy is expended by hydrodynamic drag ...
Low shots often hit/interact with the bottom before reaching maximum potential distance. Ground-effect exacerbated lift perturbations can also occur ... further attenuating kinetic energy.
High shots also actually gain energy again as they fall from the point
of maximum trajectory. i.e. the puck gains potential energy relative to
the bottom of the pool. Sometimes that results in high shots going farther
than low shots on average.
This effect depends on the puck, its rotational dynamics, stick, shot-style, bottom composition, pool slope, etc etc
The energy to overcome gravity occurs at shot-release.
The important point is that low shots can be released faster, with less
effort, and from awkward shooting positions ...
and are therefore potentially far more dangerous to "low-flying heads" than high lofted shots.
I don't have calculations to share ... High-speed film does confirm this hypothesis ...