Could Warwick's "pseudo-CDR" effect on his W be used for items, like Morello or ER?

Referring to how Warwick's Blood Hunt active cools down twice as fast while he's not hunting any targets. I feel like that mechanic has potential to be used in other things, and the first things that came to mind were Morellonomicon and Essence Reaver.

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Morellonomicon

Fiendish Codex (900) + Lost Chapter (900) + Amplifying Tome (435) + 765 = 3000

+100 Ability Power +400 Mana

Unique Passive: +10% Cooldown Reduction Unique Passive: Damaging an enemy champion with an ability or pet attack causes your abilities to cool down 15% faster for the next 3 seconds.

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Essence Reaver

B.F. Sword (1300) + Caulfield's Warhammer (1100) + Cloak of Agility (800) + 400 = 3600

+70 Attack Damage +20% Critical Strike Chance

Unique Passive: +10% Cooldown Reduction Unique Passive: Critical strikes restore 3% of your Maximum Mana and cause your abilities to cool down 15% faster for the next 3 seconds.

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Essentially, they're counterparts in regards to being "big CDR" purchases, both granting 10% flat CDR plus an additional 15% pseudo-CDR while you're fulfilling the item's intended play pattern. I wasn't sure if 10% would be too little for needing to actually be doing something, so I nudged it up to 15%, but what do I know.

I left the Grievous Wounds off of Morellonomicon because, honestly, an item as all-purpose as Morello really shouldn't have Grievous Wounds on it. Mortal Reminder is at least a bit more niche with its focus on bonus armor penetration.

Could possibly make an alternate upgrade for Lost Chapter that provides GW in exchange for some of Morello's more generalist statistics, if you really wanted to.