I like cleanse because if they have very much CC, i can just be like "nope" including to ignites etc. If used well, it is much more useful than most other summoner spells.
Zhonyas and Banshees ill admit are more AP oriented...... However the Edge of Night/Mecurials Scimitar although the scimitar and Cleanse both would only work against the slow.....would nullify Fizz's ulti as well and are AD items. Same with Maw but that has varied effectivenesses.
Fizz is a troll on a pole for sure, but same as Rengar you can counterplay him if you have the reflexes for 1, the willingness to be open minded for 2. Always learn, pay attention to what they do, if you have any CC abilities...... Make note of them. Are they skill shots? Are they targetables? Did you know Blitzcrank if he launches his E empowered fist on Fizz before he jumps, the knock will still go through and knock the Fizz off his pole?
There is a lot of interactions etc that you can use and do. I was telling you the ways that you can counterplay (inwhich items and SS counterplaying is still counterplaying.... Ignite vs swain and mundo and aatrox and vlad etc..... Same as Thornmail if the enemy autos, morellonomicon for mages, and mortal reminder/executioners calling for AD.....) you just have to think and keep a cool head.
EDIT:
And yeah, i did point out the side stepping the ulti with the "just dodge" because it is something you can do that can mess them up. It is perfectly logical reasoning and you should be learning how to dodge anyways because you are not supposed to be going "oh look! A fizz ulti! Let me go walk on/into it!". If this was lost on you however, you can just continue nitpicking to try and not learn or see any reason. Then if i ever see you i will play Fizz and know that you will never beat me because you do not want to learn even though you made this post on the forums saying you want to learn.