Having played every edition, I'll say this: Previous editions did something similar to what Kid proposes, i.e. the fastest going first and going often. This meant that the street sam or the adept would take all their actions and then...combat is over.
That's it. The fast guys killed everyone who is NOT fast. The mage, the hacker (then decker), anyone who wasn't augmented like the combat monsters did nothing. It became an arms race to see who could get the highest numbers first. And while the mage could get the spell to boost his reflexes, he either sustained it himself (thus gaining a penalty) or used a sustaining focus (which, in previous editions, meant that someone on the astral could drop a fireball on the group and cook them while remaining invulnerable). This really left the slow folks out of the fight.
Here's an example: In first edition, the limit to the number of actions in a round was four (similar to what we have now). Our group had a physical adept by the name of Drenaline. While we were in Vietnam on a mission (long story), our group noticed some bad guys up ahead. Initiative was rolled, and Drenaline ran forward, killed everyone of the bad guys, found another group of baddies, killed them, and then climbed a tree to scout out more targets. And this all happened in a single combat round before anyone else could take actions.
The current system works much better to allow people other than speed queens (or kings) to take part.