Earlier quoted context omitted.
Brass wool is often just copper plated steel, and will damage the plating. Thus, pin holes in the tips iron, nickel, or chrome plating begin to pit the copper core. https://www.eevblog.com/forum/beginners/brass-sponge-has-rui... Anecdotally, all wool seems to accumulate abrasive crud, various amalgamated solder waste, melted plastics, and trimmed bits of steel etc. Best of luck =3
That's certainly a concern, but it's completely ameliorated by buying real brass wool. The stuff that came with my (apparently genuine) Hakko 599B is non-ferrous (and is therefore not steel). Refills are Hakko part 599-029. Soldering iron tips are usually made from copper with a thick iron plating. On Moh's hardness scale, iron doesn't care much about what brass thinks. :)
The tip on my soldering iron is perfectly fine though.