As a Mid lane main who plays a lot of Zed, I feel so irrelevant come late game/5v5 team fights

Every ranked game i've played so far on this account i've won my mid lane hard and got fed at least 3+ kills before 12 minutes and sometimes got solo first blood tower BUT THEN some fed Kai Sa or Caitlyn or insert ranged champ who built two crit items sitting behind in front of their Lulu or Janna and takes in all their shields and buffs and hard carries. I just cant get damage down without getting blown up or getting cc'd to death by support then getting blown up, yeah I try to wait out their cooldowns and when I do I can kill at least the adc or support but by the time I wait out cooldowns in a teamfight, most of my team is dead or about to die, so I kill one person, then die myself in the teamfight. And it almost always the case that when that scenario happens the only kill my team got is the kill I got. So idk. Unless there some get rich quick trick to stomping teamfights as Zed that I don't know about, I might stop playing zed and play someone with more utility and sustain like I see a lot of others doing in the mid lane. I know Zed's laning phase is one of the most broken if not maybe even most broken in the game atm. But after 20-25 minutes I feel the champion and his value as a whole take a sharp downward spiral unless the enemy team has a no utility or point and click cc support. If anyone has late game Zed knowledge i'd like to here it. Or tell me if I'm right in feeling how hard it is in team fights and later game. But I mean i've never been higher then gold 4 so theres probably a lot of things im doing wrong and have the wrong attitude towards.