It'd be a tiny tiny fraction of your load reduced, but a significant impact on functionality.
At my last building we hooked circ pumps up to the hot water loops to help with that. It still took several cycles of the auto-faucets to get warm water over if no one had used the bathroom for a while. And that was a short (<25 foot) run, with a pump pushing it. Lotta water in the lines, not all of what comes out is on the hot side, and not that much comes out.
I'd say it's this.
AND add to that the empty uninsulated drywall and metal stud constructions of most commercial structures built in the last 20 years, and stuff like unheated suspended cielings and interstitial spaces, the hot water has to overcome the rather cold supply pipe too. And and the hot water just doesn't work because nobody's willing to hold down the spring-loaded automatic fixtures, or wave their hand like an idiot under the already touchy IR sensor for five minutes.
Epic contractor fail:
Friends had a very expensive house in NoVA built (IMHO the workmanship from their builder was shoddy all the way around...lots of "WTF?" mistakes for a million dollar home).
Somehow the master bathroom toilet was hooked to the hot water supply. Gave a new meaning to taking a steamer.
Some builders do that intentionally in warm or steamy climates, places like VA or TX, or just when there's normal shower/bathroom steam. The warm water fill in the tank prevents cold condensation/sweating on the toilet tank that could leave stains, or water dripping to the floor.
I also see some people hooking up their refrigerator/freezer ice-makers to the hot water lines because the hot water holds less dissolved gas, and makes clearer and better tasting ice, even though it's a "waste" because now the freezer has to overcome the injection of warmth into the icemaker.