As discovered by many folks with solar hot water heating feeding the input of a conventional hot water heater, injecting hot water into cold water input of conventional hot water heater damages the enamel internal tank coating with repeated temp shock that fractures coating resulting in premature tank rusting and tank leakage failure.
That's very odd.
For one series water heaters are very much "a thing" in buildings, even residential.
Second, and more importantly, that doesn't actually make sense unless people are doing odd things.
The 2nd water heater should still be connected to power/heat and set to not below the safe level (50c, ~120f) iirc) or you risk "fun" bacteria. In the case where the first tank is not currently heating worst case is however cold the water from the utility is, but that's no different than effectively normal operation. Since this level of cold water must already be designed for that should never be an issue. If the incoming hot water is within say normal-ish operation (60-65c, 140-149f) even in the case that you completely empty the capacity of the first tank AND it has heated to maximum you're not looking at too much of a difference in temperature delta and some people run their tanks that hot anyways so again, no real difference.
The only scenario I see causing more thermal shock is running the first tank extremely hot which risks damage to both tanks. Per literature from the people who make, install, and service tanks it's less the thermal shock at high temperatures but more that it accelerates hard water deposits which cause damage. Not sure the mechanism behind it or if there are perhaps wrong.
Regardless, if you installed a thermostatic valve between tanks you could limit the incoming temperature, and resulting thermal shock, at least in the second tank.
How risky (bacteria wise) is it for the first tank to possibly sit below 50c for hours when hot water is used overnight? No idea. I *feel* like having the 2nd tank *always* be hot enough mitigates that but I'm no biologist.
The question that comes to mind is are we seeing "touched it last syndrome" (often seen in IT work, you fixed the malware the user opened so clearly the broken keyboard is your fault). Have people been having issues with new tanks, or with a tank that they converted for re-use that may already have had damage, or maybe the anode rod was never replaced.