If you don't do it, you may still find them eating around the crusts, for instance if you cut a sandwich in half, or even gnawing through a single point on the sandwich's crust and then leaving behind a crust-rind when they're done.
As a parent, you're then left with no other choice than to eat all of the grilled cheese rinds yourself, so you don't tend to push too hard on the childish habit.
But that's because it was gross industrial bread to begin with, and the crust was just drier and unpleasant.
But I also remember eating sourdough with its chewy crust and loving that.
Cutting off crusts is very specific to bread that is bad to begin with, I think.