Well, that sounds like it could be very complicated since buffs and debuffs and such are being slinged around at an increased rate. That and we would have to reveal stats for all foes including bosses to find out where they are on the attack speed list.
But the biggest issue is when an ally is knocked out by a foe in the middle of the round. The entire plan would be interrupted to have to remove them from combat, choose a replacement fighter/pokemon to put in their place and so on, and giving them a new set of actions (unless you want to imply that defeating slower targets cockblocks them from having their turn which seems quite dangerously overpowered when considering potential bosses). A single round in a battle would take several times longer to complete and be exceedingly more complicated.
So, at the moment, I'm not terribly excited about that idea as it is. Sorry.
As for Speed having a purpose, Gem and I already put the modification to Crit using speed as a critical factor. He also wanted to give some sort of evasive bonus for speed as well, but we never got into that yet...
Basically, it sounds realistic/neat but it just doesn't sound feasible at all in the context of this forum base RP, especially with the slowed down rate we're kinda having now due to circumstances of both avoidable and unavoidable nature.
Oh, and a very Happy Birthday to you AB!