Nuclear powers mostly avoid conventional wars with each other because: Actual victory (which is presumably the Big Payoff being sought, when a country goes to war) would be too likely to suddenly turn to ashes, because the other power felt "sufficiently threatened" and started using nukes.
1) You have other nations as co-conspirators who know that you nor they have nuclear weapons.
2) You have other nations who are not co-conspirators who don't know that you don't have nuclear weapons.
2 a) Some of these nations might claim they have nuclear weapons.
2 a i) The original lie is perpetuated because it's useful.
2 a ii) The original lie is perpetuated because the other nations fear they might actually have figured it out.
2 b) Some of these nations will want nuclear weapons and invest vast resources into a program that can never eventuate. They will be forever trapped in submission.
2 c) Some of these nations will be allies who purchase "nuclear weapons" but they are never allowed to verify them.
3) You have the general public indoctrinated in the belief that nuclear weapons exist. 3 a) It would be easy to control your own populations because they fear nuclear war.
3 b) It would be easy to control other populations because they fear nuclear war.
3 c) "Why bother, we don't have nukes" mentality.
---The common belief is that the world would be doomed by the firecrackers going off. But the world is very large and life on earth has survived worse. The power in any threat is the idea of "what might happen". Ideas like "we might ignite the entire atmosphere of earth", "radioactive fallout will spread throughout the earth", "a nuclear winter will destroy life on earth". Such existential fear porn easily embeds into imagination when accompanied by visual imagery that we've all been exposed to. Whether nuclear weapons were real or not, the "nuclear deterrent" would be just as effective.
Conventional weapons are extremely destructive and devastating. Germany and Japan got to taste that in their defeat as the allies ruthlessly firebombed defenseless urban centers [0][1][2].
[0] https://www.bbc.com/news/world-europe-51448486 [1] https://www.bbc.com/news/uk-england-43546839 [2] https://www.elsevier.com/connect/maps-reveal-how-japans-citi...