In all cultures, there is an expectation that you have to provide a name for yourself that is intelligible to the culture you're interacting with, both in written language and in speech. If your name is Albert and you are going to interact with many Japanese speakers, you'll have to call yourself アルバート in writing and pronounce your name as something like "Ah roo bay toe" to fit in. If you have a name whose pronunciation depends heavily on tones, such as a Mandarin or Vietnamese name, and you are going to interact with speakers of a non-tonal language, you'll have to come up with a version that you're happy with even if pronounced in the default neutral tone that those people will naturally use. If your name is 高山, you'll have to spell it as Takayama.

Similarly, if you're going to create an identifier for yourself that is supposed to be usable in an international context, you'll have to use the lowest common denominator that is acceptable in that context - and that happens to be a-zA-Z0-9. Why the Latin alphabet and numerals and not, say, Arabic, you might ask? Because Chinese and Indian and Arabic speakers are far more likely to be familiar with the Latin alphabet than with each other's writing systems.

For logins, we're already used to the fact that they're expected to be in Latin. Having them in the native alphabet is more trouble than it's worth (one system supports it, another breaks etc., easier to remember one, in Latin, across systems) I'd be irritated though if I couldn't use my native alphabet in the user profile for the first name/last name

I think restricting the allowed characters should apply to usernames and other unique identifiers that can lead to confusion (admin vs аdmin with a Cyrillic "а"). So if I write my name as "José", I should be able to make an account called "Jose" and still enter "José" in the name field, if such a field exists in the first place. Although I'm not even sure about this.

If you're saying that "José" should be accepted as an username, shouldn't "Борис" or "김" or "金" also be valid?

It makes sense to restrict the alphabet for things like usernames that should be unique, should be easy to read for security reasons and should be correctly handled by various types of backend software.

I'm not from the US and my name isn't ASCII, but I wouldn't mind spelling it with the English alphabet, even in a name field.

I also don't understand how English has 26 letters, but letters like "é" in "José" or "ï" in "naïve" appear as normal letters. And if I write "Jose" instead, it would read as offensive. In my language that uses Cyrillic, the letters of the alphabet are all the letters we use, period. It would just be wrong to borrow a letter from another alphabet, even if it's the same script, just because someone's name includes it in their language. I have a friend from a neighboring country that changed one of his Cyrillic letters when he came to my country. I would do the same if I went to his country and they didn't have a letter we have.

As someone with non-ASCII name, I'd like a unicode whitelist (system wide if possible).

And special features to mark cyrillic or other for-me-dangerous characters.