If you just used a cooldown on an origin with a long cooldown, you can switch to human or an origin with a short cooldown and after the cooldown is done, switch back to the original origin and their cooldown wont have to recharge

When switching origins, all powers and their data is removed. That means also cooldowns will be removed. This has nothing to do with a shorter cooldown running on your other origin, it just happens as a side effect of the origin change itself.
I have no intention to change this, because changing origins is not something I'm balancing around - it's not intended to be used in the truest sense of the mod (which is also why the Orb of Origins is not obtainable without installing a data pack for it).