Hero bets river with nuts and air and makes villain indiferent to calling or folding. Now let's imagine that villain isn't capped and has the nuts 10% of the time(let's assume, in order to simplify that the villain's nuts beats our nuts ). Now, if we bet exactly pot and are balanced, we will have the "nuts" 1/3 of the time, and we are bluffing the rest. Now villain can always fold or always call with his bluffcatchers (the ev for bluffcatchers is 0) and he will always call with the nuts, obviously. Now his ev for that spot is:
ev=0.1*(pot*2) -> pot stands for the initial pot size.
And our ev is: ev=0.9*pot-0.1*pot=0.8*pot
So it seems to me that the our maximum ev for betting river has a inverse correlation to the amount of nuts combos villain has. If he has 0 combos (classical spot) we can claim 100% of the pot.
Dont really have a concrete question. I know the conclusion was obvious. Just want to know what you think about this subject.

Isn't the idea that we don't lose when we have the nuts? By definition, if villain can have "the nuts" we can't have them.

In the example I gave our nuts is simply a hand to strong not to value bet(it wins against 90% of villains range!). Your definition of "nuts" is correct, I was just using the term because my example is a derivation of the classical spot nuts and air vs capped range.

I think I remember a thread about Isildur passing on value bets on draw completing rivers vs Durrrr a few years ago. In one hand in particular, Isildur had Aces and tens when a backdoor flush came in. Isildur checked it back and lost to a Queen high flush that was obviously hoping to check raise the river.

I mention this because of the big effect that the opponents ability to raise has on value betting frequency and thus bluffing frequency as well.

The less nutty hands your opponent has, the thinner you can value bet and the more you can bluff. The more nutty hands your opponent has, the less you can value bet and the less you can bluff.