The shown instrument does not have Berliner Pumpen, a valve system I wrote about here:
viewtopic.php?p=255358#p255358
I happen to have a single horn with Wiener Pumpen plus crooks and slides for Bb, A, F#, and F. If nothing else it is different from instruments with rotors and Perinet style pistons.
The airpath isn’t too bad, and research converting frequencies and their amplitudes into 3-D graphic maps show that the legato connection between notes are smoother on Wiener Hörner than on conventional horns.
Why are Wiener Pumpen no longer in widespread use? Why are they no longer seen on trumpets, valve trombones, baritones, or tubas?
Each valve slide connects to two pistons, which have to move exactly in sync. That is a problem of its own, today only addressed by a few makers of very costly double or triple descant horns.
But my take is pragmatic at a lower tech level. The pairs of pistons represent quite a bit of inertia to be handled by long and thin brass push-rods (on the horn), by the elaborately shaped and heavier push rods on this present C baritone. These push rods will either flex or be heavy. The action isn’t as precise as with rotors let alone pistons.
Disassembling these Wiener Pumpen for maintenance also is risky.
K