Eh, not really. I really vary what I play a lot. I'll do like 2 rounds of SWAT then a Dominion game or two, then some CTF and/or a Team Regicide ... I'm really all around the playlists, so my K/D is bound to be low. I'll check it out once in a while if I'm logging onto Waypoint for kicks, but it doesn't really effect how I play.
For instance, on CTF I might be in last place on my team by points, but the kills/assists I got before the enemy grabbed the flag simply don't count for much. That doesn't make me any less important to the team. Heck, I went 15-0 in CTF twice on Ragnarok. Enemy never got the flag beyond the landing zone of the man cannon. And that only happened twice the whole match. I was still in last place on points, but could have been an entirely different game had I not defending the flag like I did. The same is true in other matches where I die, keeping 3 enemies busy while my flag runner gets the score. My K/D goes down pretty hard there, and I don't even get flag score points, but he never would have made it if not for my interference.
K/D can be fun, especially among friends to ****talk, but it means absolutely nothing unless all you play is slayer. Even then, assists should be factored in when judging someone's skill.
I sometimes look at it to get an indicator of how I'm doing, but I don't really care enough to let it get on my head. Hell, I've already mentally braced myself for the fact that getting things like the Plasma Pistol to Master level are gonna make it take one huge dive.
Rarity is best Pony. Yes, I'm a Brony. No, I'm not gonna try to get you to watch the show or dislike you if you don't. People can like different things.
Indirectly. The care of it comes from the fact that doing well (getting kills and dying less) is more fun to me. I don't care what the particular number is, but the more consistently I am going positives, the more fun I am essentially having.