He finally had his chance, as late as it came, and he didn't take the decisive course of action.

A very good point, he did the same mistake already in 1809 marching to Vienna instead of trying to finish of Archduke Charles.
However, Kutusov's army was a part of the whole Russian Army only, even in case it would be crushed, there were others approaching. I don't think it would have changed Alexander. The war was as good as won for the Russians already at Borodino there the Allied Grande Armée had already reached the point of no return. Only a sudden and quick withdrawal whould have saved a substantial part - could Napoléon afford such an action politically?