I'm a metallurgist. You will absolutely change the properties of high speed steel if you get it red hot and let it cool in air.
You'd be right that a bit that's gotten that hot will still make holes in mild steel and most aluminum alloys without issue.
Sharpening drill bits is hard- for most people that don't work in a machine shop and don't do it all the time. If you know what you're doing, its possible to do it right pretty much every time.
But if you're on garage journal asking questions about why your drill doctor doesn't work, chances are that you don't have years of experience sharpening bits and you're going to ruin a lot of bits learning how.
It's not hard sharpening drill bits on a DD at all, if one follows the
3 step directions.
I have no problems with sharpened bits on metal.
The DD sharpening stone has contact with the bit edge about a
half-second each pass, so a user would really have to crank the piss out of it, to get a bit hot, maybe it happens. If so, the user did not follow the simple directions.
When I worked in a metal shop 30 years ago, all bit were resharpened by machine, because they wanted them resharpened accurately.
Agree many bit problems come from improper drilling.