Why Mohg does it
It's clearly established throughout the DLC that Miquella's charm does not compel action, but rather inhibits it.
For example, Hornsent remains skeptical and conditionally loyal to Miquella. His tendency to carry out vengeance against us is suppressed, but not the resentment.
Likewise, Thiollier remains devoted to St. Trina, and doesn't present any strong feelings towards Miquella. His focus is mimicking her velvet. However he is prevented finding and possibly rescuing her.
So, then, why is Mohg feeding blood to the cocoon if not compelled to?
Simply, because it is a plausible means of achieving the goal, as long as Miquella hides critical information from him.
The Divine Gate is, after all, a stockpile of the dead that produces gods.
In short, Mohg is creating a new Divine Gate to allow Miquella to ascend.
But it is not possible because if all that was needed is the amassing of blood/bodies, every Graven Mass, Living Jar, Eternal City, Tutelary Deity, Minor Erdtree, the Abyssal Serpent, and Rykard would be an upstart gate.
There's something specific to the gate that only Miquella knows, and by withholding that, and perhaps suppressing Mohg's ability to realize it, Mohg is indefinitely waiting to be killed, just as Radahn is.