The system is the way it is to encourage teamplay and to draw people towards support roles. If you play as many shooters as you claim, then you should already know that actually healing or supporting allies in most games usually isnt worth the risk and is often detrimental to your own performance stats. Brink got around this issue quite nicely by offering greater reward for buffing, healing, and reviving teammates than for deathmatching enemies in the back allies.
An excellent post and the best answer yet to the OP - adding K/D stats would discourage people taking the vital support roles. As an example, in Container City, many of the more TDM-based team mates I've had are completely oblivious to the fact that clearing side routes totally changes changes the game by removing choke-points and spreading out enemy coverages - I also can't count the number of times that I've seemed to be the only player clued-in to the fact that the bot only moves if you stay nearby!
You SHOULD be rewarded for remembering the point of the mission and for showing some imagination in helping your team. The Operative, in particular, can be massively helpful without actually shooting anyone, through comms hacks and sneakily re-taking CPs whilst disguised, whilst Engineers are really helpful on defence, especially through well-placed turrets that can disrupt the enemy's route back to an objective, choke point or ongoing firefight, which can be helpful for buying time to hack objectives or set charges.
Players adopting the tactics I've discussed would appear, on a K/D marking system, to be a bit crap, when they have, in fact, been vital to team success. K/D scores display PERSONAL achievement, which is utterly beside the point in a TEAM based game. I love the fact that I can hit the leaderboards under Brink's system by playing to my class, by being the man who blows both the pillar AND the blocking bridge - regardless of how many enemy I did or didn't drop in the process.