I have a larger coop, not medium. It’s a walk-in and on the ground. I personally would not want any coop I could not walk into, but I can see an advantage for a raised coop for some people. A raised coop can be made walk-in, as far as that goes.
A raised coop can be easier to clean out. Just pull up a wheelbarrow or trailer and rake the stuff out into it.
If you are in a wet area, that is an easy way to keep the coop dry.
If space is tight and you keep your chickens in a run, the space under the coop increases your run area, gives them a place to for shade, and gives you a place you can hang a feeder and keep it dry.
In hot climates, you can keep them cooler if you design for it. However, a disadvantage in the winter may be that it is harder to keep them warmer. In my opinion, that has more to do with keeping water thawed and keeping direct drafts off of them instead of keeping the chickens warm, but you can handle that with proper design.
This has more to do with the size of the coop than whether it is raised, but you have to be able to reach all areas inside the coop. If it is not a walk-in, that can be a problem. I also like to be able to walk in mine to see what is going on. I’ve found dead chickens, snakes, and an opossum in mine.
I’m sure others will have different reasons but space, keeping it dry, and cleanout quickly come to mind.