They already can push us pretty hard through diplomacy and economic threats. That is all it will ever take for us to become obedient.
It would never be in the world interest to let a nuclear state collapse, and if it did I am sure there would be international resolve to ensure global security. The concerns over Pakistan for example.
It is in no ones interest to fire these weapons, no ones. Ever.
Apart from a 'rogue' state but even then I still fail to see someone crazy enough actually doing it and it working, I cannot invisage it happening either.
Not in our lifetime anyway.
I don't agree with your analysis in parts, if we didn't have nuclear weapons we wouldn't be any more susceptible to being pushed around than now. We would be covered by NATO, perhaps America, European neighbours and the vary nature of world nuclear power spheres and concepts such as MAD.. our tiny fraction percentage of this power is just vanity.
This weapon is just a nasty hangover from the '40s that has shaped world development and relations ever since. We have fallen by the way side, and it would be in our long term interests to not continue this path.