I built ours off the ground by 12" - put hardware cloth between the floor joists and the plywood for the floor. Not ANYTHING is going to chew through that floor! Why'd we build it this way? We've got weasels in our neighborhood - our neighbor lost most of his flock, as weasels dug underneath his 12" down hardware cloth (dug into the ground a foot!) at a corner of his coop/run - and came out through the wall at the floor/corner connection. Took him most of a summer to figure out how the weasels were getting into his coop as the hole was less than 2" diameter! (And the weasels were well fed that summer)
Some folks do it because they're not sure of the dirt in the area they're in and their disease load is potentially high (where pathogens don't get frozen each winter). And with the cost of concrete - unless you're building on an existing site - trying to put in a concrete floor for a coop is prohibitively high. Unless of course you've got a concrete mixer laying around your yard.....
Some owners are utilizing EVERY SQUARE INCH of available space for their hens due to the size of their yards or urban/suburban areas. So if the coop is off the ground, the space under the coop can hold food/water/more run space. And some municipalities restrict the size of coops/runs/etc. So some of it is for legalitites.
Some is for ease of cleaning - much easier to clean if you're not bending down all the time (for those with infirmaties or age). And if you build it just right, you can even design it to have the floor just above the height of your wheelbarrow - so all you do is roll up with your wheelbarrow, open the door, scoop the dirty litter into the wheelbarrow, shake in the new litter, close the door, roll off to your compost bin and you're done! No heavy lifting, not much in the way of straining (back or shoulders or knees) and easier to do!
Some owners build this way because their site has a definate lack of shade. At least with a raised coop, there is some shade to be found under the coop itself. Or aesthetics - often these types of coops are made to look like miniature houses or doll-house types.
Hope that answers some of your questions....