Well, considering that /f/ and /h/ fail to be distinct in at least one major variety of Chinese, and in Japanese...

why would we need an explanation for a historical change from /f/ to /h/?

It doesn't hold water. It's just a typical form of lenition. plenty of languages exhibit the same phenomenon. The example I'm most familiar with is Irish, where /f/ under certain phonological and grammatical conditions softens to almost nothing (written "fh" to maintain the underlying sound). The interesting thing is that the exact same set of circumstances causes /p/ to soften to /f/ (written "ph" to maintain the underlying sound). The sound didn't go away, but its partial disappearance became grammaticalised into what's called "séimhiú", which is incidentally appropriate as it contains an example of the phenomenon.

So yeah, the hypothesis is most likely bunk.

A similar sort of grammatical lenition is IIRC used in Sindarin, one of the languages created by JRR Tolkien who was inspired by Celtic languages.

Farina -> harina The h is mute. Its just dropped. And the f phoneme still exists

All speakers of old Spanish had bad teeth? And from all zones? Doesn’t make sense.

I don't know anything about Spanish language changes, but a change needn't have the entire population afflicted in order to occur-just enough people for it to become fashionable. And as modern trends constantly demonstrate, fashionable trends can come from anywhere, no matter how small a section of of a population, nor how silly the trend seems to be to the population at large, even as the population at large is overtaken by the fashion.

Even centuries later (1200s) the king Alfonso X the wise had to choose a main variety of Spanish among the ones that were used in the kingdom of Castilla y Leon.

So I doubt any previous change in the language was a coincidence or fashion: the population that spoke old Spanish was so big and diverse that it’s nearly impossible for them to suffer the same events.