You can still win the game for your team as Fizz post-30.

Two ways mostly: (1) get a pick with your ultimate, e.g. baron is up in 35 seconds at 30 minutes into the game, you land an R->Q->W on the enemy support to kill them as they come to ward. (2) Wait like at LEAST 5 seconds until a fight breaks out, then land an R on an enemy carry from fog.

Both require that you're confident you're not on a ward. Come late, unless I'm 6 items or 5 items and big component (e.g. NLR building into 6th item Dcap), I always keep a pink on me and look to make picks when my sweeper trinket is up. New Fizz is super reliant on R to assassinate, and the most reliable way to do that is from fog. Sweeper's is MANDATORY once you're level 9, and having a pink on you whenever possible is important so that you can camp the brush with your pink and sweep your path there so you KNOW you didn't walk over a ward on your way to the spot.

You also need to have the right team comp to team fight effectively as Fizz in the later stages of the game. If your team is all squishy, you're not going to be able to wait the >=5 seconds you need to wait to land an impact R on a carry. Your Riven top, Kha jungle, and Zyra support will just have died by then. So really I tend to never pick Fizz if I don't know that we'll have at least one beefy tank that can soak some damage on an enemy engage or engage fights himself.