Mine's elevated because -
I have 1" hardware cloth as the floor, poops fall through, it stays much cleaner than with a solid floor. The bottom part is solid on 3 sides and open on the side that faces the run. I don't have a problem getting chickens from underneath, if I need to catch them I chase them out and corner them elsewhere. If it were a concern you could add a door to keep them out once you chase them out of there.
It is very easy to harvest the poop for my garden from underneath.
coops sitting flush to the ground are much more prone to rat and mice infestations. I've had both, but not any more with my new elevated coop. No one wants these critters around but living in the city I am even more concerned about neighbors getting a perception that my chickens attract rats and mice.
As stated by others, it is also more ergonomic for me, warmer for the chickens and they like to be up high to sleep.