This doesn't seem to have any notion of power? Coming up with a fair agreement between people who have equal power over the thing they care equally about, isn't that hard.
But when one side is indifferent to something the other side cares deeply about, yet has veto power to spoil it, a Nash agreement isn't going to be "fair" in the usual sense of the word.
In reality people never have equal power over anything (what would that look like, physically?) so something like nash bargaining is an attempt to get closer to a notion of fair given this inequality
You have it backwards.
This formal game-theoretic notion of fairness acknowledges that power disparity exists and that having less power than your counterparty allows them to inflict greater disutility on you without you being able to inflict disutility on them in turn to discourage this.
On the other hand, fairness "in the usual sense", pretends power disparity doesn't exist and that, say, an armed robber is not allowed to take your stuff when you have nothing to defend yourself with. Which in reality only works as long there is a powerful third party (the state) that will inflict disutility on the robber for it.