I use the deep litter method (DLM) and my pop door is about 8 inches above the floor. I think the litter is compressed to about 2-3 inches high in this photo. I have standard breeds, too. (They're only about 6 weeks old here.)
The disadvantage of a door that is close to the floor is that litter gets kicked out.
Mine (except for the tractor, which was built before I learned this
) are all 8-12" above the floor, not because my bedding is necessarily that deep but because it really helps retain litter. THey can hop up and down to go thru the door with no problem whatsoever.
Also, it lets an inside guillotine-style door (arguably the most predator-proof) slide down well *past* the bottom of the door opening, which eliminates jamming slightly opne due to poo/bedding accumulation, and reducees winter drafts.