I play trumpet and horn, and have played both in orchestras for many years.
Both instruments used to not be fully chromatic (mainly playing their overtones) and so they'd be crooked into the key of the piece (usually). Thus, the part is transposed to read in C and the parts always end up with no key signature (or rather, the key signature of C major).
Now, I don't have any proof of this, but I strongly suspect what happened is that somebody studied a bunch of music from the 19th century and earlier, saw that parts never have a key signature, and concluded that "trumpets and horns don't use key signatures", which misses the point entirely. But they published that in some orchestration book, and it gets passed down and not questioned.
What's true is that, for better or worse, there is a tradition in classical orchestral music to eschew key signatures in trumpet and horn parts. What is NOT true is that the players themselves "don't read key signatures" or however the author in question wants to put it. Literally all other music for horn and trumpet uses key signatures. Brass quintets, wind ensembles, brass bands, jazz bands, musical theatre pits, etc. all use key signatures. And many modern classical composers are bucking the tradition and including key signatures in orchestral pieces too. So clearly, a player who is even remotely rounded is thoroughly used to reading key signatures and should have no problem with them whatsoever.
And obviously I don't know every trumpeter and hornist in the world, but I've never personally encountered anyone who is either so siloed into orchestral playing that they never encounter key signatures, or is such a zealot for tradition that they get angry about a modern composer using them. So I don't know who these players are that Thomas Goss interacts with, but they sound like clowns to me. Or maybe they're just doodling because they're orchestral brass players and they don't play much and they're bored?
In short, I fully support ditching any tradition based on old crooked natural trumpets and horns. These instruments are now fully chromatic and should be treated the same as the rest of the orchestra. And I may just be one guy, but Thomas Goss is also just one guy, and I at least play the instruments. As a direct retort to:
"... if you ask them what they really want, you'll get anything from a polite suggestion to a lengthy dissertation on why key signatures are irrelevant to horn. ..."
I really want consistency, and saying that key signatures are somehow "irrelevant" to horn makes no sense whatsoever.