The hollow nose preserves high velocity BC and gives the projectile a higher polar moment of inertia, making it easier to stabilize.
On impact, overspin/critical spin/ under spin matters not. You would have to spin the bullet several times faster to net any gyroscopic stability in tissue but then it would be over spun for most of its flight and less than acceptably accurate.
Terminal performance of small caliber bullets is due to their length. The overturning moment (yaw) of a small caliber bullet is much smaller due to this length and the bullet yaws much quicker.
Expanding bullets do not yaw to such degree because of form change on impact (expansion). The CG shifts forweard, reducing the effect of yaw in a negetative-feedback type of deceleration.