Is it possible to dive on a live enemy grenade to save your nearby teammates? It's the only way to continue on fighting apart from trying to throw it back when you are surrounded in a room.
Ah well actually, on the front of picking up grenades, it'd be vastly more reliable (In terms of the player picking them up) because the grenades are server-side, therefore they are always in the same position for everyone, thus the issue of crouch-walking in a circle to pick something up wont be an issue for them. Unlike dropped weapons which for some reason are a mixed bag of where the gun first dropped (server side) and where the gun model rolls / flies away to (client side).
And at least nades don't ever disappear underground like guns sometimes do.