Comment without seeing Kerim's original circuit:
The 50 Hz transformer will be acting at 16 kHz like the inductor in a boost converter, and the antiparallel diodes in the Mosfets could be conducting during part of the 50 Hz cycle the cycle.
There will be 100's of volt of 16kHz on the primary, and as Kerim said, acceptably low ripple out with a small capacitor.
The flux density swing due to the 16 kHz will be ~ 50/16000 of the 50 Hz swing ( If 50 Hz is 1.2T, 16 kHz would be 3.75 milliTesla for the same RMS Voltage) , so core losses will be dominantly from the 50Hz, as measured values indicate.
The 16kHz component of AC in the transformer primary windings could be measured with a Rogowski, possibly causing neglible heating by skin effect.
Mhmm, there's a historical lesson for young players in here!
Back in the day, we used vacuum tubes for everything, including amplifying audio. For various reasons, speakers have always been in the low-impedance range (8 or 16 back then, 4 and 2 nowadays, the latter mainly for automotive for obvious(?) reasons), while vacuum tube power amplifiers have load impedances of some kohms: this necessitates a matching transformer.
A typical tube amp, you can run at full rated power, day in day out, at any frequency in the passband, without anything overheating. That is, equal voltage at 20Hz or 20kHz will be applied to the output transformer. Losses generally decrease with frequency, because Bpk decreases faster than f^alpha rises, though it does depend on the exact Steinmetz parameters the core material possesses.
Well, "typical" might be pushing it, amps of course spanned the gamut of quality and specsmanship (or lack thereof) as much as anything ever has; but suppose a platonic ideal of something rated for the usual range and all that, and at least cromulently designed, okay?
We can model core loss with the modified Steinmetz formula: \$p = B^\alpha F^\beta\$, with typically \$\alpha\$ around 2 and \$\beta\$ around 1. An "ideal" lossy material (as in having eddy currents) has exactly these parameters, corresponding to a constant resistance "shorted turn".
Real materials don't have constant eddy currents, but skin effect instead, the impedance of which generally increases as \$\sqrt{F}\$ -- a diffusion process. This might put \$\beta\$ near 0.5 or 1.5, or something inbetween when considering a wide curve-fitting range. Real materials are also nonlinear, hence the \$\alpha\$ differing.
In any case, the lesson is, because B decreases so fast with F (at constant V), and the exponents tend to be what they are, losses tend not to go up with frequency, and indeed can go down.
Putting it another way: we might run such an inductor at high frequency, but we need basically the whole thing we would need at a lower frequency, to meet similar core loss requirements. And such a big core necessitates just as much wire, so we have no win by running at high frequency. We prefer a lower Fsw simply because it has lower switching loss (and those losses can be fairly high such as due to leakage inductance, also inevitable from the copper requirement), since we can't take much size out of the magnetics -- or we at least need different materials (thinner than mains-frequency iron, or other alloys) to do so.
Another point of historical reference: it was some DEC minicomputers, desktop PDPs I believe, had a rudimentary switching power supply -- the design was quite basic in terms of switching behavior, but it saved just enough efficiency to be worthwhile compared to a pure linear design -- which used a laminated-iron choke for bucking. I don't remember the particular ratings or values though. Probably something like 5V 10A, and Idunno, a couple mH? Might also be using finer laminations to help reduce size. Probably a lot of other products too, but this vintage computing reference happens to come to mind.
I'm assuming materials other than mains-frequency electrical steel are strictly unavailable, so there's not much to gain by raising Fsw. In this application, it mainly pushes carrier + sidebands well enough above signal frequency that it's easily filtered (as said, with leakage and a capacitor, and hopefully/preferably an R+C to dampen that in turn).
I am a bit curious (if not to the point of incredulity as others apparently have been) what really is available, or with what difficulty. If trade with India is available, but India makes (or imports themselves) ferrites, is that not a thing? Perhaps there are restrictions on materials, even as seemingly basic as ferrite, or equipment containing it. I guess it would be interesting to
make some from materials; all that's needed is Zn, Mn and Fe oxides of sufficient purity, a press, and an electric kiln. (Preferably they would be, well, the whole process: sintered, ball milled, pressed in molds with binder, and not to mention ground, tested, and process optimized to mimic common materials like N97 and etc. Perhaps processes this elaborate aren't feasible in the country for various reasons.)
Whatever the case, most such issues are largely out of ones' control, and the engineer must make do with whatever is available. I might not know the particulars, but it's a very unstable region, generally, an unfortunate state of things for many (often not good) reasons, particularly by several large actors.
Tim