the question is: does 3 or 4 switches (they could be mosfets igbts or scr's ) in series actually have lower losses than a single switch driving a pwm duty cycle into a small inductor instead of 3 or 4 switches in series driving multiple transformer coils. -- almost certainly not.
The switches are not all in series, the separate inverters run in parallel across the incoming dc. Only the transformer secondaries are in series. A very important distinction.
You are quite right though, about the total kVA rating of three or four transformers being excessive, but the combined magnetizing current need be no higher than a single transformer using high frequency pwm. So no load idling power is very comparable for both methods.
My own four transformer 5kVA inverter has a zero load idling power of 34 watts, and less than 1% measured THD.
Third harmonic is by far the largest and its down by -41db.
What you might be missing is that the four inverters diminish drastically in size with each successive stage. Only the largest 50/60 Hz square wave inverter runs at significantly high power, and switching losses will be negligible. Second stage only runs at a third of that, so additional losses of successive stage when combined are correspondingly less.
Conduction losses are pretty comparable, pwm requires a series choke, but a hard switched square wave inverter does not.
Multistep only has one very serious disadvantage, the cost of winding all those transformers. Technically its more than competitive for idling power, efficiency, and THD with high frequency pulse width modulation.
It gains most in advantage as the power level risess, but loses out in all the extra components required at low power levels.
Its always been a commercial failure, but only because nobody could manufacture multistep and be price competitive in the power ranges we are mostly interested in around here.
But for home construction its a winner if you use recycled material for your transformers, and the required power level is perhaps 5kW or more. This is not armchair theory, many of these have now been built and are all running successfully without any serious problems.
On the other hand many novice home constructors have had continuing ongoing blow ups with high power home built inverter projects. Nothing wrong with pwm in principle, but it all becomes a lot more critical in layout and details when trying to drive a large number of parallel mosfets at 20 Khz plus.