There are a few issues here:
1) Monsters have very large initiatives in the book. Most monsters have high Dexes compared to previous editions and many monsters get a +2 or even +4 bonus on top of that.
2) PCs only get a good initiative with a high Dex and/or Improved Initiative/Quickdraw. For many classes, a high Dex is a sub-optimal ability score to make and maintain high.
3) Attacking first decreases the number of enemy actions per encounter. For example, if it takes 5 rounds for a PC Ranger to kill a specific foe and the foe wins initiative, the foe gets 5 attacks before the Ranger kills him. If the foe loses initiative, the foe gets 4 attacks before the Ranger kills him. Over the lifetime of an encounter, this can add up.
4) PC Wizards are more effective if they can target multiple foes early on. Once combat starts and melee opponents get into melee range, it tends to become more difficult for a Wizard to target more than one or two foes at any point in time. It happens, but not as often as in round one unless the DM spreads out his foes every single encounter before the encounter starts. If the Wizard loses init, the 3 foes on the other side of the room might be interspersed amongst the party before the Wizard gets to act.
So effectively, the game system is set up so that most enemies, including minions, get at least one attack in before they die. Winning initiative changes that to an "at least zero attacks in before they die". Granted, most foes last for many rounds in most encounters, but if the PCs win initiative, they tend to also decrease the number of rounds of the encounter.
And, it is not necessarily just one round less of an encounter for winning init. A 12 round encounter can be finished in 9 rounds due to the PCs winning initiative because of other variables. For example, if PC 1 takes out a foe quicker, the PC might not have to stop to take a Second Wind. This in turn allows him to attack instead of healing on a given round which might in turn kill a different foe. It can become a snowball effect.
Bottom line: It's not that winning initiative in 4E is so important, it's that not losing it every single encounter is what is important. With the high monster initiatives, having PCs with high initiative to counter this PC disadvantage can easily save a lot of resources and allow the PCs to have an additional encounter before they need to rest (or allow PCs to not be TPKed in a tight situation). 4E is a game of offense and healing, not defense. Any game element that adds to the overall group offense is good for the group.