Many Mexican cheeses are fresh, and “designed” not to melt when heated. They keep their shape; they don’t ooze and run. This makes them ideal as a cheese to stuff baked dishes with. Not many non-Mexican cheeses will act like this.
For those who can’t get them, there are workarounds such as not putting as much cheese at the end of baked burritos, etc.
Halloumi won’t melt when heated, though the flavour might not be want you want in Mexican food all the time. Dry-curd Cottage Cheese, Feta (well-rinsed to reduce the saltiness). Ricotta made from whey (not whole milk ricotta). Or really, whatever cooking cheese you have to hand, but just place it in such as way that doesn’t do anything to encourage it to melt out all over the place.