Desertengeneer. Minor Disagreement, As a shi%$^ input to a xformer can cause it to "Sing", overheat, or burn a winding open.
Nonsineasodiol waveforms poise a big problem for transform input. Example (Extreme case) if you applied a 120 VAC sinewave to a 10 to 1 stepdown xformer, you get a nice 12 VAC output. If you were to apply a 120 VAC squarewave you would get a positive spike with a short decay to zero then a neg spike decaying to zero (Delay will look like a RC curve. The output of the transformer is zero during the plateaus (Eout is dependent on rate of change – there is no rate of change for a square wave except durning the leading and lagging edges. This leads to rapid distruction of the Xformer as Current is only limited by the DC resistance of the winding, Very high, as opposed to the higher X sub L reactance. UPS typically have a very poor output waveform with the cheaper ones having a sharp leading edge..
As you pointed out the output is typically a pulse modulation of sinewave controlling the on time. It is the transition from on to off that creates the problem (as you pointed out). Also as you pointed out this sharp transition (Composed of very High freq) is what causes the eeeeeeeeee sound.
I would ask the manf to provide a waveform of the output under MAX recommended loads.
Cost, size, and Weight (emphasis on COST) are the determining factors. A true Sinewave cannot be produced by a switcher PS unless that output is rectified and used as the DC to a RCL, or Xstal controlled oscillator and applied transistor amplifier. For High current this is rather large and costly (also low effiency).
Might be cheaper to buy a generator.