Do you think Ukraine would have used nuclear weapons against Russia? How do you think Russia would have responded to that? Do you think that would cost fewer than a hundred thousand Ukrainian lives?

Once again, nuclear weapons can only be a deterrent if your enemy believe you will use them and everyone knows that no nation state has the stomach to use them. Russia doesn't have to fear MAD and yet it is still deterred from using nuclear weapons. What makes you think that Ukraine would choose MAD over their current predicament? Because if Russia doesn't believe Ukraine is willing to commit to MAD, Russia can still invade. It certainly changes strategy, but over the years many nuclear powers have been involved in arm conflicts without using nuclear weapons, including in conflicts against other nuclear powers.