Mobile number login is even worse! Why do I need to share my mobile number for something where you don't need to have it!
I think you got this the wrong way around.
Their whole point was that you could be confident the people were real because they were tied to a real Facebook account.
This was the first month of Pokemon Go years ago. I haven't heard of it being an issue lately but I also haven't needed to create an account in a very long time.
And a bit over a year the same thing happened. New Pokemon Go account -> log in -> no game. With Google account has been working since.
So, my experience is two tries in the span of two years it did not work.
I’ve gotten rid of Facebook, but now my account name is just a bunch of numbers.