>If pronouncing Xochimilco according to English orthographic conventions is important to you as a matter of principle
No, not to me. I speak Spanish natively, but even I don't know how to say that. My first guess would be "Jochimilco", but I'd have to look it up (I'm not going to). I'm just saying that having Xs in weird places would not stop an English speaker from inventing a "wrong" pronunciation on the spot.
>But it’s a Mexican place name that has a canonical pronunciation that is not difficult for English speakers to approximate, so I can’t really see the point.
"Mexico" itself is also not difficult for English speakers to approximate, yet they don't. Clearly approximating the local pronunciation is not how foreign speakers decide how to pay toponyms, and that's fine. That's how languages are shaped.
My point is just that it makes no sense to get hung up on speakers not pronouncing loanwords "correctly". If we're going down this path, we should also complain that Spanish speakers write "fútbol" instead of "football", and that tea is called "tea" instead of "cha" and spelled "荼". We should demand that words be crystallized in their pronunciation and orthography when they cross language barriers.
There aren’t any hard and fast rules about how to pronounce loan words. I agree on that point. In your original post, though, you seemed to be entirely dismissing the option of pronouncing the word according to an English approximation of its native pronunciation, which is an approach that’s equally valid (and is what English speakers often do for quite a few words).
>In your original post, though, you seemed to be entirely dismissing the option of pronouncing the word according to an English approximation of its native pronunciation,
When a pronunciation is already widespread, yes. "Axolotl" is not some new word; lots of people know the animal and call it "aksolotl". If we were talking about, say, some obscure Chinese village that suddenly became very relevant in the English-speaking world, I would not insist to pronounce the pinyin spelling of its name as if it was an English word.