Except when the transformer blows, it isn't possible to fix it, and a replacement would cost more than a new machine.... The only parts you can really replace are the diodes, and depending on the machine, possibly the current control.
Machine like a carburetor, you can replace one or two small parts cheap and easy, but the main (and most important) part is not fixable or replaceable.
Where as for an inverter, all the parts can be easily replaced. I could find 99% of the parts in my welder in an afternoon..... It's just a matter of finding the blown part, remove it, and solder in a replacement.
Much like an injector system, all the parts can be easily replaced, economically....
Just because something is simpler, doesn't mean you could fix everything as easily......
Although an inverter is more likely to die, virtually anything that blows can be easily fixed, even if the manufacturer is long gone. A transformer is less likely to go, but most failures are the end of the machine.....