@RRK
I am fairly certain (looked it up a while back, can't remember) that my solder does contain copper. And I can confirm that if it erodes at the rapid rate that is does now with copper added, I can only imagine that it would erode unusably fast without copper.

For the wet sponge vs brass wool:

The wet sponge is softer, so less abrasion to the tip, but it cools it rapidly, creating heat shocks. So when still generally acceptable for lead soldering (where the temperatures use to be in the 300degC ballpark), the higher temperatures required for lead free means the shock becomes way more significant problem. Plus if the tip is not hot enough to evaporate the water instantly (when someone is wiping the tip when it is already cooling down - never do that), it promotes corrosion of the iron layer.

The brass wire wool is a bit harder, but still should be softer than a good quality tip, but it does not thernmally shock it. For higher temperature lead free soldering (around the 350degC tip) this becomes very important.

Good quality tips use way more than 2 or 3 layers, usually the copper body is coated with Ni (via some intermediate) to get hard, strong surface, mainly at the high temperatures, with iron coating on top of it to form a  layer easilly wettable with molten solder. Nickel alone forms rather hard oxide layer on it (that normally is what protects it against further corrosion), which makes it hard for the solder to adhere to.

So in other words quite complex structure for any DIY.

The "900" style is so common, you can find all kind of tips for it, from really bad garbage till really good quality, obviously more expensive, ones.
Don't forget this format has its origin as a rather good quality and also not that cheap stations, so good quality tips are still made for it.
Only because it became a format chosen for cheepeese clones, the market is also flooded with garbage quality product offerings you have to dig through...

@Medved Any practical examples where cleaning the tip with wet sponge have done *any* harm due to a thermal shock? Or you are just theorizing?

I am doing it all the time for many years since modern soldering tools has become available, with tip temperatures of 320-350C, also it is a standard practice for the industry, no one uses brass shavings seriously, as it is less convenient. More, most soldering stations come with soldering iron stands having wet sponge plate embedded.

Also, there is no point to use a sponge (or be it brass shavings) on a tip with a temperature below water boiling point as the solder will obviously be solid too, and all sorts of cleaning (short of a file or a sandpaper will be ineffective!