I've found a couple of current Weller wood burners for sale. One says 25 W and 900F (480C). The other says 750F (400C).
You've got me thinking, and I see I don't know how hot the soldering irons and guns I've used, could get. If I don't have a wet sponge handy, I'll use dry paper, such as a napkin, to wipe a hot tip. The paper won't smoke. It will pick up solder and oxidation but probably won't be even lightly browned. By contrast, if I touched my hot wood burner to wood, I'd get a puff of smoke and leave a dark brown mark. That doesn't prove a soldering iron wouldn't get as hot as a wood burner if I gave it enough time.
A couple of years ago, I replaced 18 crossover capacitors in loudspeakers. I was reluctant because it seemed as if I were no longer any good at soldering. I bought a new iron and it was as easy as pie.
I think if solder won't cling to a tip, it's hard to transfer heat to a joint for a good solder connection. It seems to me that if a tip gets to a certain condition, it may not perform very well even after sanding and tinning.
I suppose an iron takes a minute or longer to heat up. If I use one and think I'll need it again in a couple of minutes, I'll leave it plugged in. It could sit too hot for hours, being used only a few times. I end up with a damaged tip, and I'll think I can't solder.
In cases where a semiconductor manufacturer said a lead could be at soldering temperature only a few seconds, I'd ignore conventional wisdom and use a gun. When you take a soldering iron from the stand, it may be much hotter than necessary. You touch it to the joint, touch the solder to the joint, and wait for the heat to flow through the joint and heat the solder to the melting point. Meanwhile, heat is traveling up the lead to the semiconductor.
With a gun, you pull the trigger and press the solder to it. The instant you get a drop of solder on the tip, you touch it to the joint. You know you're just above the melting point of solder, and contact lasts about a second. Fastest gun in the west!
My first battery iron was a Wahl Isotip, about 1974. I liked it so much that I bought another, in the 1980s. They would heat up quick. My fingers were pretty close to the tip, for precise control, like a pencil. They were unlikely to overheat anything.
I see nowadays they use 3 AA NiMH cells. That's great, just pop in fresh batteries and keep going! One advertises 8 watts and 900F. Another, far more expensive, advertises 9 watts, 12 seconds to operating temperature, and a limit of 450 F. That's the one I want!