My Information concerning this topic (A320):
- 120 ft/min considered as normal touchdown rate
- 360 ft/min certified up to MTOW (that is the already mentioned 6 ft/sec)
- 600 ft/min certified up to MLW
Extensive inspections required for overweight landings with 360 ft/min or greater.
Beyond that, everything was said already in the posts above (reasons, risks & benefits etc).