I care about win streaks, but not as much as overall win-loss record. I think we have 5 losses on the board, so 45-5 in our last 50. I'd rather be 45-5 with no good win streaks than 40-10 with a really good win streak in there. However, keeping a good streak going is fun. It raises the excitement of the wars as the streak goes. I agree with OP in that sense. War win streaks are fun. For those who say they don't care, I recommend experiencing a few
I don't agree with OPs proposed "tie breaker," though. While he thinks of it in terms of all th13 wars, perfect ties in all th13 wars happens very rarely in terms of percentage of wars. Instead, the proposed change would much more often impact lower wars, including clans who intentionally keep their halls low, engineer, roster engineer, etc. While I think it is a better tie breaker than the often suggested "attack time," I still don't like it.