What is wrong with the concrete as is? SURE makes it easier to clean out the shed area. Maybe get some rubber mats if you think the floor is too hard. You might find used mats cheaper than new, or buy a-mat-a-week, to get the floor covered eventually.
I would think covering with dirt would just leave the area mucky, since dirt won't drain well after getting peed on or rain comes in the sides. Turn shed into a fly attraction and then breeding ground with moisture.
I agree, I wouldn't just leave a run-in with plain concrete, unless I knew they would only be using it very intermittently.
I have rubber mats in my run-in. It's not like my horses are running around in there, so I don't feel that "slippery" is a quality that I am concerned about. Plus you can get different textures of rubber mats. I have both solid and the holey kind (the holey kind near the front & outside for drainage from rain)
And yes, you could put dirt over the concrete, as much as you want. (well, wait... would the dirt be going up against the metal sides of the barn? You don't want to rust out your barn) It depends on what KIND of dirt too, because sandy soil vs. clay soil would make a huge difference as to how that worked out for you. But where does the urine go? The urine will build up and the ammonia smell will start to become quite noticeable... you'll have to have a plan to deal with that. Another option would be to bed it like a stall. Either way, you'll have to clean it out periodically.
One thing I've noticed since I've put the rubber mats in my run-in (I used to have just screenings) is that they hate to urinate on them. They make the effort to walk the 10 feet to go outside. They still poop in there, so it doesn't eliminate clean-up, but it's a lot quicker to pick up a few piles off the mats than to sift through shavings/straw looking for wet spots etc.
They put dirt over concrete in Madison Square Garden when they have horse shows, so it should be OK. The only thing to think about is drainage, if rain blows in or horses pee. I think stone dust, that is compacted would be better.
We would have to add a vent fan to pull the hot air out of the roof area.
Rubber footing is a great idea. I wonder if you could use burlap sacks filled with this stuff, lay them down side by side, add a top layer of solid mat, and mak your own comfort stall for a fraction of the price. LOL