You're not wrong, but what matters for Putin is whether or not the Russian public believes they lost. They know it isn't going easily, but they don't know they have no hope of winning and that Ukraine will never be theirs. A difficult war is one thing, but retreating in shame and failure is another.

When they stop recruiting soldiers and instead they come home with nothing gained, Putin will look like a fool and will be overthrown. They will tolerate a brute, but not a failure.