I don't think deaths should be kept track of. Otherwise people will log out to avoid them.
I also have a problem with a "kill" count, because of the way STO keeps track of kills. The way it works now, if 5 people focus fire & kill a ship, Each of them get a kill on the scoreboard. Unless that was changed, it seems to me that all you have to do to inflate this number is to use a large number of AOE attacks., or constantly switch targets.
If I understand the system correctly, it doesn't work like t hat. You need to deal a minimum amount of damage to the target, but I am not sure what the minimum is - I think it has to be half of the target's hull or something.
I think an easier & more accurate way to run a leaderboard would be to keep track of only a few things, like damage & healing. I further believe that there should be 3 leaderboards, 1 for Tac, Sci, & Engi, It could be further subdivided into PVP & PVE, & space & ground.
This could be an additional sorting / finegrained view option. My idea is ultimately that we track tons of statistics, and allow different views on them, and some of them are used for a small reward system in form of accolades, trophies, and item/currency rewards. A distinction along the lines of ship & player class makes sense to me here.