I'm just wondering, how fast can a French Horn play 16th notes? Like, I've got this 1 measure passage of a descending 16th note chromatic scale at 152 bpm - is that too fast? It's to be played legato. Can the performer move the valves that fast?
How long a run and how good a player? A short run of 16ths at 152 bpm is no problem A longer run would be OK for a good amateur or above. He'll have played worse in etudes.
This example isn't as hard as it looks. And if anything is holding your players back from emulating it, it isn't the mechanics of the valves.
(Obviously, don't write concertos in the ensemble of a middle-school band piece! But a short chromatic run is really no problem.)