Would you suggest that a melee attacker get to do something like a "reckless attack" action as an option? Something like that might confer a decrease to the defense pool of the attacker for a single Initiative Pass or something similar.
Well, there's already sort of something like that in the "full offense" action from Run & Gun.
I think of number of people in different threads, and an idea I had myself, separately (great minds think alike) is something like a "hasty melee" attack. Alternatively, for unarmed, you could call it a "jab" or "snap kick", I don't know what you'd call it in fencing.
Basically just -3 to dice pool to do the attack as a simple action -- additionally I'd think it reasonable to say you can't split the attack like normal, not that most people would with the reduced pool. This is based off of the quick spellcasting idea.
This does a lot to create better parity between the melee guys and firearms folks. There's a lot of things just aren't a problem for a firearms guy -- drawing a weapon, called shots & centering, activating various adept powers that require a simple action, that are a HUGE deal for melee guys.