I think it would be fun if there was an additional type of streak for killing 50 players with no healing.
Healing resets this type of streak to zero.
I don't suggest this as a means to replace the existing streak system, but in addition to.
And, at the risk of upsetting all the ECnistas out there, there could even be a 1 time secret achievement for it , like the one where you kill 10 people when you're below 5 health.