I've always felt that things like levelling and achievements are just a cheap way to extend playability, and while I used to enjoy them in games I'm starting to feel the opposite way now. Particularly when it's achieved simply by playing a long time (or doing something extremely monotonous for a shorter period of time), and has such an impact on your combat ability that it's almost required if you want to play on the harder difficulty levels. I'd much rather your effectiveness in combat is decided by skills aquired over time (such as accuracy, reflexes, and good strategy).
However I realise it's necessary to have levelling in a game like this to enhance its life, and while some players seem to care more about grinding their stats than playing well with others, they aren't all like this, and besides more players isn't a bad thing. So, I'm not against levelling in a game like this. I'd just like to see a revised system that doesn't overall boost a player's effectiveness, but allows them to use enhanced abilities or weapons when they have proved themselves capable, allowing them to move deeper into their role and away from others (such as support moving slower but having lower recoil, taking less damage, and maybe being able to carry weapons that can be dropped but not immediately equipped by the carrier).
So if it were up to me, I'd replace the perk system with one that requires each perk to properly fill its roll, and prove the player's skill before allowing them to advance to the next level. For example, the sharpshooter's headshot requirement makes sense since it requires some skill, but it should be necessary to perform headshots from certain minimum distances, and other useful tasks that the sharpshooter could do. When you gain a level you could (for example) be granted the use of a scope on other weapons, although the effectiveness of firing from the hip could be reduced, meaning while you have better long-range effectiveness you have lowered close-range effectiveness. I'm not saying it should be harder or easier to play when levelling up, but I think you should be required to slightly alter your style so that you may be more effective. Of course, you'd also need to be able to select any acquired perk level, since you may want the benefits of support but not the disadvantages of a high level one. Using a low level perk would therefore be more of an all-rounder choice - good for beginners.
One problem with such a system that gives you more varied opportunities without necessarily giving your weapons more power is that the gameplay (the AI in particular) would have to be altered so that a more skilled player would be able to handle the highest difficulty levels, even when using a 0 level perk. Altering the system so that this is possible could be tricky, as it'd require possibly giving enemies different strategies and moves on harder difficulties, for example.