While good in theory for only some skills, it isn't very good in practice for all skills, cooldowns should only be placed on very powerful skills, (That one being Lunar Lunatism.)
Overall it doesn't make interactions with PvE or PvP very fun, I do think that some skills should keep cooldowns however, as it is a good way to limit some of the ways they were super strong, those ones being:
Screamer (screaming tome)
Burn Up (Skyburn)
I shouldn't really need to explain the reasons as to why it just doesn't work outside of "It just doesn't" from just practicing, so if want to revert it at that, that's fine. But I wrote up a few reasons in a spoiler below.
Skill worth: A skill can simpily just be an extension of your combo, something like sidecut, wazabane, hanging, Ryemei, Wind Slasher, Rabbit leap etc. etc. Since most skills now are only worth the SP at rank 5, this puts the amount of skills someone will possess at a very low number, repeat skills was never a problem I find.
Cookie Cutter strategies: You could wall out a hexer's damage almost entirely by staying out of their Menov's range and then waiting for them to try and poison you, once that is done you can cure that poison with anti-toxin or purify poison, and yet not get punished for doing so because now, one of their poisons is on cooldown, this would merely just adopt a counter-meta to every single class, rather than create moments of weakness.
Overall I think it's the right idea, but in it's current state it is just simply not fun to play with. I am interested to see how this goes.