It's not about being more deadly, it's about staying alive. Remember that actually getting to use your swanky Dodge or Gymnastics skill when someone is blasting at you costs you an action. Unless your Reaction alone is better than the Agility + (Firearm Skill) of most bad guys, and unless you know for sure you'll kill every bad guy in sight and no one will still be around to attack you after your action is over, you really, really, want extra Initiative Passes.
Yes, it's awesome to think about a guy that shoots three times faster than the opposition, but remember that everyone gets their first shots and then guys with multiple IPs get theirs. So if you're a super badass Shadowrunner fighting against four security guards, for instance, the odds are good you'll kill one or two in the very first action, sure...but then what? Then they're getting to roll attribute + skill against your attribute (+ nothing, since you already used your action and won't be using a proper dodge), to try and shoot you full of holes. That's normally a contest you'll lose. It's especially a test you'll lose if you're comparing your Reaction attribute to them (while trying to stubbornly avoid boosterware).
See the issue? It's simple math. Extra IPs -- or enough Edge to fake it -- are absolute necessities to anyone who plans on making himself a target in a fight. Even if you're only duking it out with low wage rent-a-cops that don't have extra IPs themselves, it's the nature of a Shadowrunner's job to be outnumbered, so you'll have lots of incoming fire. You want at least a second IP, so you can declare a proper dodge and get to use all those points you spent on combat skills.