If such welded cores were ONLY in microwaves, then you would be 100% right. Unfortunately; many audio amplifiers also have a welded core. It is only about the fact that the production of such a transformer takes much less time - just put the "E" package on the other "I" and weld what would not fall apart. And that, by the way, this is more likely to happen
heats? In this case, it is secondary - the lower cost overcomes common sense.