I always consider myself wrong when faced with something I don't understand.
So, in pondering this whole thing, it has dawned on me the best use for the shower/bathroom sink cold water.
It can easily sit in the designated container until it's time to add water to the toilet.
Easy, effective, local to the problem by inches.
It could also, if insistence on following through on a thought is indeed an insistance:
The shower valve pipe thingy that runs water back to your fresh water tank, the one that essentially absolutely eliminates the water heater discussion, could just as easily fill a toilet bowl.
And now we're on to leaky toilet ball valves.