I think a class mainly used to supply others would help to speed up gameplay in a positive manner. The class would have items such as health, blocks, and ammunition that can other players would be able to collect, but would have no firearms or a weak sidearm for defense at most. A speed increase compared to other classes would make this "support" class more capable of defending itself and more effective in performing its role within the game.
When in the middle of a map, the only solution when out of supplies is to die or run all the way back to the end of a map to a command post. A class that has minimal arms but a wealth of supplies would help alleviate this irritating aspect of the game.