This is currently a bug that hasn't been addressed. Ascension does not receive faster cool down after use paired with spirit of inmost light. Hopefully soon this will be fixed.
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#destiny2
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A long while ago ascension lost it's class ability status due to breaking pve and pvp. In revenant they allowed it to work with some effects but not all of them. Because it wasn't given class ability status yet and was just given the ability to work with certain things I'd assume this isn't bugged.