The active stain removing ingredient in Bar Keepers Friend is just cheap old oxalic acid. One can buy a lifetime's supply of oxalic acid crystals on the internet for the price of one container of Bar Keepers Friend (which is an expensive cleaning product).
If scouring wanted as well, then there are dozens of cheap products in the supermarket to do that bit.
Again, oxalic acid is widely used in the yachting industry for removing stains on all sorts of things, including on stainless steel, waterline stains on fiberglass/paint, rust stains on sails, etc. as it is otherwise non-aggressive. If one needs it to stick while it works make a paste of it with wallpaper paste, for example.
I wouldn't rely on it for sterilization, it is mild (although poisonous to humans if enough taken), and am unaware of it being used so.
Wow, I'm going into the cleaning products business, I didn't realize there were so many people willing to throw their money away on cleaning names (there again I have seen the TV advertisements aimed at them
).