When daisy-chaining an UPS to another, the downstream UPS can easily overload and trip the upstream UPS because of that.
It has not happened yet. If downstream UPS likes the source, it is not going to switch to battery, and battery charging will Not be happening because downstream UPS had it charged already long time ago.
------------
I bought three UPSs, all them used independently; but I had to stop using all of them. They all had a capacitor whine that was driving me crazy.
Your run-of-the-mill UPS is likely to either be offline, which forwards the input to the output, or line-interactive, which can compensate to an extent under or over voltage conditions with a regulator. If the input current characteristics are outside allowable tolerances, they can't compensate and must switch the load to battery to continue powering it.
This is the key to this whole discussion. I guess it boils down to existing line-interactive designs, why they can't work with simulated sine as a source.
A dual-conversion (online) UPS is almost certainly more robust as far as what kinds of inputs it can accept (though as GP noted, they're more expensive, and they're also less efficient due to the additional rectification->inverter).
This one surely should "like" simulated sine wave as a source and don't drop to battery?
But why would it require grid-like sine wave and not go along with whatever is the source, provided source can still be used to charge its batteries? I saw no answers yet, and this "why" is the very key to the discussion.
For example, a common topology in offline UPS is that the inverter and the charger are the same circuit driven differently[0] - so you can't charge the battery while the inverter is carrying load. This is popular at the low-end because you have literally half as much UPS, but makes what you're describing impossible.
Another common issue at the low end is that the inverter isn't thermally sized to run non-stop, they know they can cut a corner because your battery presents a finite and known duty cycle.
There are ways around this, but at some point you end up fixing the wrong problem - eg, it's cheaper, safer, and more resilient to buy a transfer switch instead of uprating two UPS to be capable of daisy-chaining.