I honestly think this is the reason for the whole Trump-US-Russia friendliness. In terms of nukes, it's the US and Russia, period. Russia is in grave danger of becoming a failed state, with all the problems that entails with respect to nuclear weapons as you described. So the US is going to do everything it can to try to make sure that doesn't happen. Russia cannot become a failed state, almost at any cost.
Ordinarily, it would be jarring to have the US suddenly cozy up to Russia in this way, but Trump's personality and potential criminal liability provides useful cover for the shift. Note the cadre of US congressmen who traveled to Russia on July 4th. That's not Trump.