Which he won't do if mutually assured destruction is credible. He's not going to destroy the world including himself and everything he loves for Ukraine.
Once there are doubts that use of nuclear weapons will be punished, then all bets are off.
It’s a bad idea to bluff in situations like this, because when the obvious bluff is called and you are forced to back down, it makes enemies more likely to test all your commitments and “red lines”.
While Putin might not be willing to risk MAD either over Ukraine, it’s a lot more believable that he would than that the US would. There have been direct kinetic attacks on Moscow and parts of Russia have been invaded. There have been assassination attempts against people close to him. This is not some far away conflict for him. He’s already taking on a huge amount of risk, a lot more than the US has taken on in a long time—even in WW2 there was no direct attack on the continental US.
Personally I don't see any real chance of nuclear escalation over Ukraine on both sides. The war needs to end but to do that Putin needs to be given a way to deescalate and claim a win at home. But that can only be allowed to happen if Ukraine is made safe and secure once again and if Putin is willing to swallow that. And I see no evidence of that being true.