Other than having likely a lot of dissolved minerals, resulting in high TDS, what else about your tap water makes you think it's poor quality? Does it also have high phosphates/nitrogen content - or other impurities that make it low quality? If it's simply hardness, that shouldn't make the water quality "poor" unless you're keeping plants/fish/shrimp that absolutely require soft, more pure water.
The water we have here in Phoenix is a combination of surface and subsurface water; the surface water does not have issues with nitrates nor phosphates. It's remarkably good (other than aesthetic concerns which get quite complex) but for the high TDS- mostly sodium, sulfate, chloride, etc.- a bunch of ions that aren't really useful in the context of aquaculture. But, of course, without running a controlled experiment, I am unable to say whether there would be any positive results would that I were to use water with lower TDS.
An example: a 55-gallon with a single 2" oscar (a freebie from a big-box store that, at the time, was in danger of being an ex-fish), and there is virtually no evaporation; with 10-15% water changes every week, TDS is over 1000 ppm as measured with a digital TDS meter. That's how bad it is here. As a kid, when I had more fish, we had 80 ppm TDS right out of the tap, and that was mostly carbonate hardness. At least the fish could make do with the calcium.
If you are happy to do a 50% weekly water change then great, sure that happily resets everything (but, to be clear, the fish are still swimming in 50% diluted sewerage!). But why 50% and not 60%, 30%, 5% or some other arbitrary value? And why weekly and not daily, or bi-weekly or monthly?
I think this is an excellent way to put it, thank you.
We rely upon test kits and meters for ammonium, nitrite, nitrate, pH, hardness, and temperature. Once these are satisfied, what other parameter(s) may fall out of whack, and how do we measure them to optimize the conditions for our charges? If I can't measure it, is it even a real concern?
If it's hormones, OK- I'll throw up my hands and keep doing water changes rather than purchase that $180,000 LC/QQQ for measuring salmon gonadotropic-releasing hormone, I totally get it. Y'all are the gurus at keeping semi-closed system aquaria, I'm not trying to come off as some sort of a jerk. Scientific curiosity has gotten the best of me, and I appreciate the discussion thus far.