Piano keys do bounce, notice the low bass note bounce. I don't feel it because my finger has released the key before the bounce. It's normal. Piano keys that don't exhibit some bounce are typically stiff harder to play actions that are more sluggish.

That is true, but some keys can be too bouncy.

If repeating a note quickly, it's unlikely that the key would be allowed to come all the way up before being restruck, so the bounce wouldn't happen.

Any time there is mass, gravity and/or spring force, and damping, some oscillation will take place. In a grand action, there are several coupled masses, several springs (including felts), the force from gravity, and damping, mostly from the lossiness of the felts.

I've noticed the degree of bounciness tends to vary quite a lot in both acoustic and DP actions. I guess it results from the springs trying to return the key back up as soon as possible (allowing fast repetitions), and the weak damping at the top.
I liked the ES8 quite a lot when trying it in a shop, but was in fact bothered by its pronounced bounciness. The CA series actions were much less bouncy, and awkwardly the CN29/39 also, despite declaredly the same RHIII action as the ES8. The FP90 action is a bit bouncy but not excessively. I noticed some ES110 owners complain over this.