Football is similar to boxing, the helmets don't help because the concussion results from your brain rattling around in your skull, and which cannot be prevented in that sport.

It is a different situation, though, the helmets in football have evolved into weapons people use to slam their head into their opponents as hard as possible. People have argued LESS protection would be better, because it would change the way the game is played.

The same incentive does not exist in skateboarding, however. You want to land the trick, not hit someone with your helmet. Additionally, even if the helmet does not prevent a concussion, it will keep you from cracking your head open on the pavement.

Skate helmets lessen shock leading to concussions, even if they are not tested/rated for that. Football's issue is different as the helmet leads to more/harder head-first hits.

Also football helmets are designed for multiple hits to the same location... where as bike/skate helmets are designed to absorb a single blow and be discarded.

While true, helmets do prevent other types of injuries such as skull fractures. They're still worth wearing.