Brink had this, but the effect wasn’t strong enough so the ability went unused.
Overwatch is doing this with their Lucio character. He can increase the speed of every teammate in a small area around him.
Do you think this would have a place in Dirty Bomb?
If the boost required players to stay close to the boosting character, then that might promote team pushes in pubs. Would also make it fun for enemy Fraggers and Naders to get multi-kills.
Don’t really like it:
AoE effect like you describe would give a very inconsistent feel when fighting particular characters.
Guess it would be okay if a specific character had it, Imo new assault merc with average guns but the ability to get aura speed at 130-150hp for a few seconds; sort of ‘medic adrenaline rush’ from ET, without the medic part : )
Rhino with speed boost wouldn’t even be that bad, he would just go normal speed. Imagine Sparks or Proxy with even more speed, it’ll be like trying to shoot down sonic the hedgehog 
the current map pool is far to small to have a speed boost skill maybe for the larger ones being made dome/dockyard they might work