black crud appearing on the tip is NOT normal. leaving flux on the tip is also not caring for the tip properly.
You can also lower the temperature greatly (under 300F) and apply liquid flux to eat away contaminants for a couple minutes. the tip tinner products are better but not necessary.
It's the solder I wanted to leave on, but since it's rosin-cored flux must also have remained. I did wipe it off often and coat with fresh solder. As for temp, I'll definitely try lower, I think you mean 300C though since 300F is not enough to melt solder.
It sounds like either the tip is trash, or your "damp sponge" is not a proper soldering sponge. I wont pretend like i dont use a kitchen sponge myself, but you should be aware that there are like 3 or more different "standard" sponges commonly used in the kitchen. Some of them will have chemicals that are bad for the iron.
Unless fake, should be a quality Hakko tip. Fake is unlikely it's not customary to pirate trademarks in the US (it came with Hakko logo). I think I used the cellulose sponge, it's an old small one that came with my Yihua 936 station, don't know if it's high quality or not but it's meant for soldering.
We had the sponge discussion last week: https://www.eevblog.com/forum/testgear/replacement-sponges-for-hakko-888d/
If you are going to use cheap sponge, or change brands of RMA or R flux core solder for tip tinning, it may be advisable to try them on a cheap plated tip for a bargain basement 25W non-temperature controlled iron that uses Weller style straight 1/4" rod tips secured with a grubscrew before risking a new expensive temperature controlled solderstation tip on them.
Also, it would be worth trying distilled water for wetting the sponge to avoid a buildup of minerals and avoid the chlorine that is commonly added to municipal water supplies. If you are too cheap to get distilled water, use water that has been boiled a couple of times in the kettle and always over-wet the sponge then squeeze it out. The worst of the minerals will have precipitated out in the kettle, the chlorine will have boiled off and squeezing the sponge out gets rid of most of the minerals left behind when the previous wetting dried out.
I think I'll stick to the metal mesh for the time being, as far as the sponge being cheap or not, I didn't even know there were many different kinds. Cellulose by itself shouldn't be damaging to the tip, nor do I see any particularly harmful chemicals getting on it during manufacturing, though I'm not sure.
Don't think I'm desperate enough to try distilled yet. Calcium and magnesium are the main "contaminants" in tap water, a few dozen ppm, and I don't think much of that should make it to the tip surface, nor do too much harm in trace amounts. Chlorine will evaporate pretty quickly from tap water that stood there for a while, so not necessary to boil, but that would work too.
Pretty much, just a fast wipe on both sides and a check, then back in the holder.
I'll try that next time, didn't do that before since I thought a thick layer protects it better.
Could your sponge have got contaminated by something nasty? (technical term, HiHi)
Could your iron be running hot (hotter than indicated)? I run mine at 320c.
Sponge: I can think of nothing I would classify as an active chemical where I keep the sponge.
Too hot: almost certainly, that's been a ubiquitous theme in the comments up to now, my 400C probably didn't help, even if other factors were present.
Thanks to everyone for the excellent feedback I got so far. I'll try put that advice into practice when my replacement tip arrives.