I've never had the solder stick to the brass and it's softer than stainless steel so I guess that's a pretty good material for the purpose, though less readily available for making a DIY tip cleaner. I bought a pre-made one on eBay from China for <$2USD w/ free shipping. I pull the brass out of the can every so often and all the little bits of solder fall out with a couple taps.
I didn't realize the purpose of the plastic insert. That would have come in handy a couple times with my old flux bottle. I ended up gluing the thing to a piece of steel flat bar to give it a stable base.