I've tried the commercial stuff & it doesn't seem to work any better than supermarket brass wool, or Stainless steel scrubber pads, for that matter!
The hardness of Stainless doesn't seem to be a problem, at least, I've never seen any great wear on tips from it.
I've found the hardness of the stainless steel isn't necessarily a problem, either. The iron and the chrome in a tip are both very hard, and abrasion isn't the issue. It's the stiffness where you can run into a problem. If you use the finer stuff, like 000 or higher, it should be fine. The coarser wool is rigid enough to accelerate chipping/cracking of the edge of the chrome plating. The thicker wool concentrates more force into smaller areas, enough to potentially damage the chrome. I would suppose you could damage a tip the same way on a block of brass with a sharp edge.
It sounds stupid, but there's a similar phenomenon when removing rust from blued carbon steel. If you use 00 steel wool, you remove the bluing. If you use 0000, you can remove just the rust. It's the difference between theory and practice, I suppose.
Yeah, you can buy bronze wool, commonly sold in marine supply shops and whatnot. If I had to take a guess, I would think it's used to scrub fiberglass. It's super, super fine. There are also some pure copper scrubbers called Chore Boys, but there are a lot of knockoffs that are copper plated steel, too.