Finance academia is in the toilet swirling the bowl.
Referee didn't know that conditional expectation is a random variable

It's not a random variable. It's a moment.
Interesting troll. But nobody is that stupid so its a dumb troll.
Wait, sorry. I read it as conditional mean. Conditional expectation E[YX] is a constant for every X. I take back my no good and call it a day because I'm now officially doing stupid things.

This is a matter of semantics. E(YX) is a conditional mean FUNCTION (of X) making it plausible to be interpreted as a RV. However, normally the "conditional mean" refers to E(YX=x) which is a nonrandom constant.
So maybe I'm an idiot but isn't this right?
Given a DGP, the (conditional) mean is some constant. The sample mean on the other hand is a random variable.It's not a random variable. It's a moment.
E(YX) is a function of X, so it's random. Get it?

Wait... the title is totally wrong. OP, why is your conditional expectation a random variable? I mean a conditional sample mean is obviously a RV but your cond. expectation is collapsing all the randomness onto 1 point for every X.
Maybe I'm just tired and not reading things properly. My brain is asking for alcohol to wake up.

This is a matter of semantics. E(YX) is a conditional mean FUNCTION (of X) making it plausible to be interpreted as a RV. However, normally the "conditional mean" refers to E(YX=x) which is a nonrandom constant.
So maybe I'm an idiot but isn't this right?
Given a DGP, the (conditional) mean is some constant. The sample mean on the other hand is a random variable.It's not a random variable. It's a moment.
E(YX) is a function of X, so it's random. Get it?
How about we simply say that E(YX) is a RV with a dirac delta distribution (I've been doing the whole interpretation with X=x)