I always hear people at different shops talking about how steel cases tear your gun up and they all have lacquer on them and it comes your gun hope real bad. Well most newer steel case has switched or is being switched to polymer coating. And i've never had any problems with steel case out of any of my guns so far. I shoot steel in .223,.40,9mm, and .380 never had a problem. Plus i clean my gun after any amount of shooting anyways because that is good practice so i really don't know how dirty it gets. Doesn't seem to be any different then when i shoot brass.
Like others have said if it runs it then by all means shoot it up. I have a bunch of the regular tula from walmart that i've picked up here and there. I'll continue to buy it.
The only issue is the steel does not expand like brass. So you will have more carbon build up in the chamber.