I wanted to say, A small amount of mixing is possible, but this is very rare for fantasy world with different races.
Not when you factor in trade.
So long as races are trading with each other, there will be major trading ports. Where people from multiple races will reside in to oversee the large trade flow.
This is inevitable, because even fantasy settings are based around capitalism. Every race wants to ensure trade, for money and resources which confers power.
Imagine the Tolkien' or Warhammer Fantasy elves/dwarves will go to live in the first dirty puddle in human' town... This is awful to even think about.
You say that like it wasn't frequently a thing in Tolkien's universe. Heck even the Dwarves and Elves where BFF's for a time (Which is why the door to Moria, the biggest Dwarven city, is made using Elven magic - With specifically the password being the elvish word for "Friend") and even post-LotR they got back to being on good terms with each other thanks to the friendship between Gimli and Legolas.
There's also plenty of examples of elves giving up their immortality to go live with humans (Notably, Aragorn himself is a decendant of half-elves (Which are themselves evidence of human and elf partnership) and his wife Arwen is an elf who gave up her mortality to be his queen).
To say nothing about the whole thing of many people post-LotR going different places. Elves all left their cities (That were no longer being bolstered by the rings of power due to them being disabled with the destruction of The One Ring), some went back west to The Undying Lands, while others remained in Middle Earth and thus had to go live in human or dwarven cities.
Yes, this is the very basis of all modern fantasy, Tolkien's work, where it is very frequently shown that races mix together even without anything like actual trade cities (Which would further create melting pots of culture within them)
