One of the points classical and modern military thinkers make is that if you leave your enemy no choice but to fight to the death you will pay a price for that (see Sun Tzu and others). In 1973 Sadat may have only wanted the Sinai back, and Gaza not included, I'm not sure that we know that for a fact. We also don't know what would have happened had the Egyptians had the sort of military success that allowed them to cross in to Israel proper. It is highly doubtful that the Syrians would have stopped at the pre-1967 border, and if the other Arab states were winning would Jordan have sat on the sidelines? In any case for years the Arab leaders had been been, at best, not shouting the "destroy Israel slogan" but really most had, in Arabic to their own folks, had endorsed the idea. Had their forces had the ability to enter in to pre-1967 Israeli territory, it is unlikely that a stop order would have been obeyed, and giving such an order to "victorious" forces might well have resulted in said leader losing their position or life.
By their own rhetoric since before 1948 and certainly afterwards, the Arabs, as a whole, put the Israelis in a position where the perception was losing=death. That on top of the Holocaust and the various actions towards Jews in Arab countries (until essentially all left/expelled with few exceptions) made this perception a very realistic assessment of the situation. This is not to say this assessment was overblown, but it wasn't "paranoid" and based on fantasy. This is why nukes were made by Israel in the first place, as the "ultimate" force multiplier for a state that was always going to be outnumbered in a big way.
The point of this argument is that you can bet your bottom dollar the Israelis would use nukes if push came to shove - no ifs and or buts. If you (the State of Israel) are "alive" you may have to deal with international upset, but it is manageable. If you are "dead", all the international support/sympathy is irrelevant. A nice eulogy does the star of the funeral no good.