Normal mode, blind pick is full of players that have absolutely no idea how to play and have no desire to improve their play. I have over 1400 games in this mode and that's been my experience. I played that many games because I figured this mode was the worst case scenario. If I could carry here, I could carry anywhere and I think that rings true.
As a Zed, you should be very capable of carrying a game in this mode. You're most likely not using him to his fullest and not roaming effectively. Check out youtube videos for the best zeds around. There are some zeds that go 20/0 with 200 cs by 20 minutes cause they're just monsters that take everything because zed is fully capable of getting that fed. If he's fed he'll ult tanks under tower and kill them without taking more than 1 tower hit. I also suggest playing other roles as you seem to be confused as to why your team is trying to get kills off you and more importantly, when you SHOULD let them get it. 5 fed players is better than one. If you are up 4/1, maybe you should let the adc and jg have a kill?