This game was initially about resource management and didn't need cooldowns.
Then people cried they couldn't catch sorcerers and streak became the first skill in ESO to punish you for spamming it.
Non-sorcerers didn't notice and kept spamming their skills happily.
Then ZOS removed softcaps and added the champion system and everyone got infinite resources and could spam anything they wanted to.
Then people cried they couldn't catch dodge rollers so ZOS put a cooldown on dodge roll
Then people cried they couldn't catch sorcerers (again) and ZOS put an even stricter cooldown on streak.
Then ZOS changed gap closers so that it's impossible to escape them and anyone that can spam ambush could catch anyone no matter how many times they dodge rolled or streaked. Why didn't they do this before they nerfed everything to hell?
Now the only way to kill a good player in PvP is to burst them down because anyone who knows that they are doing can still build for infinite resources.
So to answer your question, YES. As the game is now, it needs cooldowns. Back when this was a game about skill and resource management, back when we had soft-caps and you couldn't get equivalent of three 5pc set bonuses worth of cost reduction out of one champion tree, no we didn't need cooldowns.
Without softcaps, the controls have to go somewhere. If you dont limit resoruces, you have to limit skills. Ever wonder why there are so many cries for nerfs now?