Steel wool is generally much much finer and more ductile than the bristles on a stiff steel brush. Steel wool is just a thousandth of an inch across so it's totally fine to consume a few fibers so long as it's not the extra course stuff. Even then it wouldn't be as bad as a bristle off a steel brush.
From personal experience as a dishwasher, old steel wool tends to lose little pieces as it gets more and more brittle. Pieces would get caught in the rivets where the pan handle attaches. I was yelled at more than once because of that—but how else do you clean a pan?
> I was yelled at more than once because of that—but how else do you clean a pan?
Steel chainmail is awesome for cast iron, and probably safe for anything steel wool is safe for. For pans with coating (enamel or nonstick) where that's not safe, soap, water, and sponge works (sponges have the same shedding problem as steel wool, but usually higher contrast and harder to miss and fail to rinse out when they do shed.)
I concur about the steel chainmail. I washed dishes in a New Mexican Restaurant when I was younger. The worst was the 30 quart bean pot. The starch and the beans. The chainmail made short work of it.
But focusing in on the rivets, there are two ways to look at it. The remaining fat that has undergone polymer-type conversion due to heat is seasoning, not dirt. Or if you really want to get in there, probably an ice pick.
Have you ever tried it? The forces you're applying are completely different. You're squeezing it against the wires of the grill, and it's all one connected piece of metal. If it does break, it will tear, not splinter. Plus, you want to wash off the crud you loosen anyway. Also, it's dirt cheap, You wouldn't keep an old one around for very long.