“What if giving up has just as strong a deterrent effect as winning? I have no evidence this is true but we should act like it is.”
The most common argument for taking a hard line on the Ukraine war is that Putin is a bully who must be pushed back and fully rebuffed, so that he won't try something like this again.
But what if, hypothetically, this deterrence goal is already achieved? What if the war has already gone so badly for Putin that he would never risk getting into such a situation again?
People have this idea that Putin could stop the war at any time and retreat from the occupied territories, and that his refusal to do so shows he still hasn't learned that war doesn't pay. But I think this is a mistaken belief. If Putin were at this point to simply admit full defeat, it would be a huge blow to him. He could well lose power, and perhaps even his life. Maybe Putin would badly prefer to end the war, but has no realistic way of doing so that preserves his power at home. Recall that he initially thought he would win the war in a few days. In this model he made a big blunder, and now can't see a way to get out of the situation.
If we consider this possibility, we should also consider that future wars may already be sufficiently deterred, even if Putin is allowed to keep the occupied territories and claim victory. That would let him stay in power, but it would not make new wars an attractive prospect, since he now knows they will be far harder and more personally dangerous than he first assumed. In other words, the deterrence that a defeat is supposed to deliver may already be in place without the defeat.
If we are indeed in this situation, then continuing the war is a bad path that causes more death and destruction without a realistic route to a significantly better outcome. It burns many lives on the battlefield to achieve little more than we could already have.
One could argue that a better outcome is still possible: fight long enough to force him to accept defeat. There are two objections to this. First, we must weigh what is gained from this against the enormous cost in other people's lives of trying to achieve it. Second, if admitting defeat would likely cost Putin his power and quite possibly his life, as argued above, then facing that prospect he may be tempted to escalate to nuclear warfare. So instead of a marginal improvement at best, this course could make things radically worse.
I cannot prove that Putin has already been deterred, nor can anyone prove the opposite. Putin cannot tell the truth about his situation, and we cannot take him at his word. But if there is a significant possibility that he has been, then we ought to think hard and with an open mind before sacrificing many more lives.