Should mages have a ''Black Cleaver''?

Black Cleaver is core on so many champions, it's the kind of item you just can't go wrong buying it. It has a bit of everything, health, AD, CDR, movement speed and armor shred. AD champions have access to so much CDR from just about anywhere, whether you are a tank, an assassin or an adc, it's so easy to reach the cap without sacrificing anything.

But mages don't have such option. If you want to get some CDR you need to buy items that don't offer much power besides said CDR. Sure you can get either Morello or Athene, but getting both is a waste, and the only benefit they give is some AP, CDR and mana regen, even though most mages don't struggle with mana anymore outside of early game.

AP Bruisers are left with Liandry, that serves a similar purpose, but they have a hard time getting CDR unlike AD champs.

So should mages have an item similar to Black Cleaver? If not, why? Would it hurt the game if mages also had such a core item? Why is it safe for AD to have access to so much core stats on a single item but not for AP?