If your water has any alkalinity at all, you’ll be more interested in learning the solubility of the metal carbonate salts rather than the metal it’s self since that’s how the metals will go into solution. Even so, with water 60C warmer sitting in your pipes, you might double or triple the metal’s solubility in the water. The next thing you’d want to know is do you have lead pipes? Where I live they don’t exist anymore, and even copper is on it’s way out. If you do have lead pipes you shouldn’t really be drinking any water flowing through them; worrying about how much more lead gets into the hot water from the tiney amount of contact time and length of unsuitable piping is sort of like worrying about whether you smoke light vs regular cigarettes - you’re screwed either way.
The amounts of dangerous metals in proper piping are only present in trace amounts anyways, which shouldn’t be dangerous… there’s more potential for your water supply to have bad water at the source (which is regulated) than for it to become dangerously contaminated flowing through 15 feet of pipe for a few seconds.
And once again the scale you see in water tanks (mostly from calcium bicarbonate) has been precipitated out of your water during heating, hence this water has less of these minerals in it when it comes out the tap. And the reason it precipitates out is that the water cannot hold more than a certain amount of these minerals at the temperature it gets heated too, so it’s not gonna pick up any extra when it flows through the heater tank. If your water is depositing minerals already, it’s not going to pick up any more even if you dumped 50 pounds of it into the tank. Not to mention that calcium/magnesium carbonates and bicarbonates aren’t going to hurt you anyways.
For that matter, neither will copper or iron in the amounts leached into a few feet of pipe - people purposely take all kinds of metal supplements daily. And to be picky, there will be one hell of a lot more metals leaching out of your pot or pan once you start frying or boiling at the really high temperatures than will come out of your water pipes at relatively low temperatures… and then we go scrubbing those metal pots nice and good afterwords to expose more new metal for the water to suck out next time, leave a bit of soap residue on them, and so on…
Lastly I measured the flow rate of my kitchen sink and the length of pipe between it and the water heater. There are about 15 feet of 1/2" copper pipe between the two, which holds a volume of 0.6L. The flow rate is 12L/minute. I also timed how long it took for the water coming out of the hot tap to “get hot” - 15 seconds.
So, at a flow of 12LPM, it takes 3.2 seconds for the entire volume of the heater-to-sink hot water pipe to clear, and by the time the water is hot enough for me to stick the pot underneath it, that volume has been replaced almost five times. The water going into my pot has a total exposure time of 5 seconds at 60-70C in those copper pipes. The metals that would have leached into it overnight are long gone before I even grab a pot to fill.
Disolved gases like chlorine will come out of solution faster from heated water, which most would consider good; even so the chlorine concentration is too low to be dangerous. Most of the bacteria that are human pathogens are mesophilic, dying off at temps above 45C… the thermophilic bacteria that may be in your water heater, if not already dead from the cold initial temps and chlorine throughout their stay, don’t seem to be a problem either.