The new paper purports to deal with those criticisms. To my limited understanding it appears to be an argument against how the Hamiltonian is currently formulated in Verlinde's theory than a proof against entropic gravity.

I am curious if there could be any theoretical reasoning why gravity can't be emergent, rather than experimental..

Could someone explain, what is meant exactly by `emergent'? What is the antonyme?

For example. I mean can't we assume all standard quantum model implies all quantum phenomena are emergent?

A reason that is theoretical must be backed by experiments. You cannot have one without the other without entering the religious realm. And you cannot have a completely mathematical explanation of reality because your axioms must have experimental backing.

As I understand it, emergent means the behaviour of a collection of entities that comes about due to their interactions in a way that is not predictable from a full theory of its constituents.

The opposite of an emergent theory would be a reductionist theory.