On the contrary, I think 'we' (the US) use them every day as leverage and a deterrent. We just don't need to detonate them anymore. I think there is more to it than them being just a trump card. You only get to use a trump card once.
For the few entities with nuclear weapons, it's MAD. We would only play the card once, since it would be the final round of the game with that entity.
Somebody could come up with something tomorrow. Maybe a bacteria that can populate the ocean, which precipitates carbon from CO2 in the air, and drops little pellets to the bottom. Probably not a real practical solution, or even a good idea, but it shows how things could rapidly change if the right tech comes along. They wouldn't need to get everyone together - just a petri dish thrown into the ocean.
We are still thinking of solving today's problems with today's technology, which I agree is futile to get everyone on the same page.
As far as nuclear bombs, we don't really seem to be using them much anymore. They are just trump cards in the mutual assured destruction game.