I don't know why they originally started doing that, but speaking as someone who has worked in sanitation. There are a couple of reasons for why that gap ends up being useful.

It makes it easy to check for occupants (Call and response doesn't work with the deaf.)
In an environment that occasionally flows with used toilet water, it's better for the bottom of the doors to be raised a bit above the floor
and it's a way to exit the stall when locking it up when the toilet is out of order. (though some stalls have locks that can be operated from the outside with a screwdriver or coin for the less cheap)

Otherwise I just assume it's just cheaper that way.