>That's because in English we get it via Spanish

The misconception is that words enter "a language" and not individual people's minds. Most English speakers have never heard the word "axolotl" spoken in its original pronunciation, nor are they familiar with the orthography that spells a "sh" with X.

>Spanish, which doesn't have ʃ (although interestingly, it was just in the process of losing that sound in the early 17th century).

I don't know about 17th century, but some dialects of Spanish certainly do have that sound now.

>Otherwise, what are you going to do with Xochimilco?

In English, X at the start of a word is typically pronounced like a Z, as in "Xanadu", "Xanax", and "xylophone". I don't think anyone would bat an eye if you read it as "Zochimilco".