Those Muslims already hate Israel. They already believe that Israel is mercilessly slaughtering children. This is a simple choice A or B scenario. Choice A, Israel capitulates, leaving their enemy intact. The propaganda continues, Israel kills babies etc. Choice B, Israel gasses the tunnels destroying Hamas, and enslaves the remaining Gaza population. The propaganda still continues, Israel kills babies etc. The propaganda doesn't change. It doesn't require more validation, they have all the validation they want. They already have the videos of mangled children under rubble, schools, hospitals, everything.
You're conflating two different arguments. 1.) Israel using a WMD would absolutely have made a difference for the Palestinian propaganda efforts in Western countries, countries whose support Israel still needs. 2.) Even if Hamas had been fully destroyed or vanquished, a new terrorist organization espousing the same ideology would have emerged in its place. The same is not true for Germany, Japan or Franco-era Spain.
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I mean short memory only if they're vanquished. There will always be holdouts, but irrelevant holdouts. Spanish civil war: Franco wins and there are still radical holdouts trying to loudspeaker their propaganda. Franco just ignores them and rightfully only refers to them as bandits. They disappear in a few years. None of Israel's enemies have been vanquished (nor has Israel of course). They've been bloodied up in a serious of wars spanning decades, not defeated. Machiavelli wrote about this: if you are to defeat an enemy you should defeat them in whole, or else they only seek vengeance.
And that's point I'm trying to make: vanquishing Hamas alone accomplishes almost nothing; Israel would need to vanquish
the entire Arab world to have a chance at rooting out the ideology of its opponents in similar fashion to how the Allies pacified Germany and Japan, or to how Franco got Spain under control. And that is very obviously never going to happen. You're pointing to historical examples as a blueprint for what Israel should do while ignoring that the situations cannot be compared.