No, it is not. Russia was attacked by Ukraine multiple times and nukes are still not used. India, Pakistan and China are in various stages of conflicts with each other for decades and all of them are nuke-enabled super-powers.

There are three points of having nukes:

1. Deter other countries with nukes from using them against you, or your military ally.

2. Prevent total annihilation in the war. You can lose the war, but not too much.

3. Burn the world to ashes. Very few countries can do it. It effectively forces the whole world to make sure that this scenario does not happen. So you can be sure that scenario where Ukraine conquers Russia and completely destroys it - will be prevented by the very Ukraine supporters. They don't want to live in the nuclear post-apocalypse, because there are scenarios where Russia fires every single nuclear missile on every major city on the Earth. As Putin framed it: We will go to heaven as martyrs, and they will simply drop dead.

America lost several wars, recently they lost Afghanistan war and right now they're losing Iran war. They won't invoke nukes to overturn the table, they'll accept the lose.

Except that it's a bit more complicated than that. Russia has nukes and is under attack from Ukraine, and while in the past they sabre-rattled that they would use tactical nukes if there was ever any incursion, they haven't done so because they know that would cause the whole world to retaliate.

Then there's nuclear defenses - if a country would have an effective anti-ICBM system (like Star Wars or whatever), it would make a nuclear counterstrike ineffective and end Mutually Assured Destruction. On paper anyway, in practice there are no perfect anti-ICBM systems, and they're effectively cluster bombs so in theory after the initial launch they can break up into half a dozen "dumb" nukes. Good luck hitting those.