Usually this burnt residue starts higher up on the tip above the part of the tip that is being used. Gravity pulls any solder bead down (and you ought to be in the habit of NOT cleaning/wiping the tip before putting it up, as other posters have mentioned). And the flux tends to wick up the side of the tip above the bead, where it burns.
If you see how I solder, it would make you ill. I primarily use a CF tip, which is a bevel that only wets on the cut face. Normal modus operandi for me is to ignore the burnt residue unless it gets so bulky it reduces my view. Because the sides of the tip don't wet, the black residue builds up all the way down the sides. The tinnable face is never affected. As we speak, it has a jet black crust over the chrome and I have used it that way for several big soldering sessions without touching it. If I see bits of this residue break off and fall onto the board, it really only bothers me if it's jammed between pins, and I'll pick it out. If it settles somewhere else in the flux pool, I just assume it will freeze there and be no worries, lol. Or if I clean the board, it will be washed away.
The CF tip is unique, though. Because of the shape, the tinnable area always is very well protected, and the crust is very well bonded to the chrome layer. The cut face and the chromed areas are separated by a sharp corner, so the two shall not mix. And the tinnable surface is a flat oval. Any solder bead on the cut face tends to spread in a meniscus that protects the entire tinnable surface. In most use, and more importantly while in the stand, the cut face is held pretty much level/horizontal, so there's no part of the tinnable surface that tends to get dry (and form crust). On most other tip shapes, the crust will form over parts of the tinnable area and slowly creep down and impinge on the working surface and will eventually start flaking off in huge chunks.
Whenever I do eventually get around to cleaning it, swiping it on brass wool removes 95% of it. Lightly scraping with the end of a bit of brass tubing will get all of it without damaging the chrome.