So, all i can think about are:
Udyr - Obvious reasons
Tryndamere - upgrading tryndamere's ultimate just gives him more fury and makes his lowest health go up a bit, so it's not worth it to upgrade more then once
Shaco - pinkward used to not upgrade shaco's ult (AP shaco) because the ult didnt matter that much
Ekko - Ekko can delay upgrading his ult to upgrade it exactly when he has to use it so that he can trick someone into thinking he has ult(because of the shadow it leaves behind him, no shadow if he doesnt have ult upgraded) so you can kinda delay upgrading your ult at level 6
Can you guys think of any other champions that dont?
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