I usually play teleport with Fizz too, not against harrassing or big burst champs on lane, in that case I take barrier, but on squishy or confident matchups I definetly take teleport, for what you just said, lvl 6 --> 2 kills bottom lane ( if the support sets the right wards, or if they engage), but if this happens, you use your teleport, you gank bot, and you die for different reasons ( you suck, their jungler is there and your bot lane sells you, you miss your ulti and E so you dont get to do damage) Then you have some big problems:
1.- You just lost at least from 2 to 4 waves of minions, that means that their mid laner is out-farming you right now, and lets be honest Fizz is not the best mid game champ if you didn't farm a lot on early game or you didn't get really fed.
2.- If you have die trying to gank, this gives 3 advantages to the enemy team: 1->Mid Lane is free to push 2->Bot Lane is free to tower dive by jungler and mid and potentially kill the turret 3-> Enemy team kills bot lane and gets drake, even maybe blue.
All this just hapenned because you just died teleporting bottom lane and not succeeding in your gank.
My point is: Teleport is risky, Barrier is not.