Having nuclear weapons doesn't prevent destabilization tactics, the likes of which the US and Europe (NATO allies) used to destroy Syria and Libya most recently. In fact it increases the argument eg the US would then have to invade urgently to secure the nuclear weapons once destabilization has occurred. Plans for securing-the-nukes missions exist for countries like Pakistan and North Korea for example.

Further, the premise of deterrence is shaken when you consider the post 9/11 Pakistan example. The US threatened to 'bomb Pakistan back into the Stone Age' [1] if they did not comply with US demands in relation to post 9/11 military action. The US was not deterred by Pakistan having nuclear weapons.

It can also do the opposite of increase dictatorship stability. It increases the value of taking control of the country if you're an internal revolutionary group. If you're one of those groups and you topple a Gaddafi or Bashar al-Assad, or the House of Saud, once they have nukes, you become drastically more powerful on the world stage. It's a very large incentive to try to overthrow them. It's potentially a giant lever of power and blackmail.

[1] "President Pervez Musharraf of Pakistan said yesterday that after the Sept. 11, 2001, attacks the United States threatened to bomb his country if it did not cooperate with the American campaign against the Taliban in Afghanistan."

"General Musharraf said the intelligence director had told him that Mr. Armitage had said: “‘Be prepared to be bombed. Be prepared to go back to the Stone Age.’"

https://www.nytimes.com/2006/09/22/world/asia/22pakistan.htm...