Well, I think one of the reasons why they didn't continue with the exact same characters was that it's been so long since Killzone 1, not to mention not many people remember much of the game besides fans. It'd be confusing to dump all that plot and character info on people who aren't familiar with them.
Also, storywise there'd be no reason for the characters to stay together besides maybe Templar and Rico. Luger goes off and does secret ops, Hahka goes to work at intel or infiltrates Helgha again, Templar probably leads a larger or just a new specops unit. Rico got promoted so now he's got command responsibilities.
Oh and yes, that is Rico as your captain. I hope he picks up a Helghan minigun somewhere, he just doesn't seem right without a minigun in his hands.
Also, storywise there'd be no reason for the characters to stay together besides maybe Templar and Rico. Luger goes off and does secret ops, Hahka goes to work at intel or infiltrates Helgha again, Templar probably leads a larger or just a new specops unit. Rico got promoted so now he's got command responsibilities.
Oh and yes, that is Rico as your captain. I hope he picks up a Helghan minigun somewhere, he just doesn't seem right without a minigun in his hands.