I have and have used leather, cork and even made a denim belt once to test. Don't get me wrong, they work well enough but when it comes to finish work they aren't quite there compared to what I can do by hand in nearly the same amount of time (if you include the time to swap the belt out and the QC factor).
And don't take this as any knock against them, I use my belt grinder often. I just feel it is a better fit for some parts of the job than others. Once it gets up past the bevel setting stage the time intensive work is done and I can take over with stone(s). I keep them right next to my grinder, so is very convenient.
A related note, I was using mine last night and was testing pressure amounts vs heat buildup and removal rate. My grinder is not typical - top end RPM is about 1200 and I normally run at half of that or less depending. But with light pressure I was able to keep removing steel without heating up the edge, continuous contact of 10 seconds. In fact it wasn't even warm. Stock removal rate went way down as well though.
And point taken about heating steel up by hand. When I was working on improving my freehand speed technique I was able to get blades hot enough it was uncomfortable to keep in contact with my palm just using the coarse side of an India stone - with oil.