Because of the focus on roles (defender, striker, controller, leader), you may want to consider the relative importance of high initiative to various party members.
Example: Strikers don't really need to go first, though there are exceptions. The leader (for buffs), the controller (for positioning the enemy and removing a few minions fast), and the defender (to help grant combat advantage and tie down a big nasty) can all go before the striker.
High initiative is only somewhat important to a Controller.
It really doesn't matter too much for the rest of the roles because it takes too much of an investment in order to really do it well for the gain.
One has to a) take Improved Initiative (feats like Quick Draw are ok, but generally not good enough) and b) have a high Dex that improves every level that abilities improve, and c) find a third way (i.e. item, feat, or class feature) to really get good at it.
Many monsters have better initiatives in the game system than the average PC. Many of them have high Dex and/or either a +2 or +4 bonus added on.
The exception appears to be Brutes which are often low Dex and no bonus.
Artillery and Controllers tend to have high Dex and no bonus.
Lurkers tend to have high Dex and a +4 bonus.
Skirmishers tend to have high Dex and a +2 bonus.
And Soldiers tend to have low Dex and a +2 bonus.
This works out to Brutes being half level+1+1/tier; Artillery, Controllers, and Soldiers being half level+3+1/tier, Skirmishers being half level+5+1/tier; and Lurkers being half level+7+1/tier.
There are exceptions to this, higher levels tend to get more swingy with a +6 delta for the same role not being unheard of at high epic, but that is the general rule of thumb. So, any PC whose main or secondary ability score is not Dex is going to have a problem keeping up. That's about 2/3rds of all classes.
Since so many classes have a hard time keeping up with initiative, it's typically not something a PC should concentrate on unless it plays to that PC's strengths based on class, not role.
Edit: Forgot to mention that higher level monsters get +1 to init for every 2 levels as well (i.e. n+1 monster might be +1 more to init, but an n+2 monster is typically going to be +1 to init compared to a similar same level monster and an n+4 monster is typically going to be +2 to init).