If the tire is loaded against the drum through vertical posts, it seems like letting the wheel "float" without troublesome play or stiction during the test might be tricky without a pretty decent linear bearing setup. I was under the impression that this was why some other test rigs suspend the wheel with an arm pivoting from the side.


Maybe. But it seems like vertical deflection transmitted through an extremely-stiff tire to a rigid load isn't necessarily going to tend toward returning to forward motion.

Think about the cartoonish extreme case of a wheel system rolling along a flat surface, which strikes a bump and bounces into the air, then lands on the flat surface away from the bump and continues on its way. That vertical deflection energy isn't returned to forward motion, even if there's almost zero damping in the wheel system; low damping just makes it take longer to dissipate (i.e. the wheeled system might bounce repeatedly). A squishier tire that produces a smaller bounce may lose less energy to vertical motion and have a higher forward speed after the bump.
Edit: And even if the system doesn't fully lose contact with the surface, a vertical lift in the system could give the tire less opportunity to push/roll off the back of the bump, even outside of considerations of hystersesis.