Why are reversible gates not used?

it relies on the motion of spherical billiard balls in a friction-free environment made of buffers against which the balls bounce perfectly

… this sounds very realistic. Nobody has actually figured out how to actually make such gates yet, they’re merely of theoretical interest. That might explain why you’ve never heard of them since engineering usually deals with practice. The premise of Reversible Computing is that when a bit disappears, some amount of heat is generated. By using reversible gates, no bits ever appear or disappear so supposedly computation could be much more efficient with reversible gates. The theoretical limit Reversible Computing claims to get around is that erasing 1 bit of information generates at least $kTln 2$ energy in heat. For a computer running at a toasty $60,{}^circmathrm{C}$ with $10^9$ transistors each making bits disappear at a rate of $5,mathrm{GHz}$, that corresponds to $16,mathrm{mW}$ of heat generation. That only accounts for a tiny proportion ($1/10000$) of a computer’s energy usage. Our current-day computers are not limited by heat generation associated with bits disappearing. They are limited by the inherent inefficiency in moving electrons around on tiny copper traces.