In a vacuum, no. In a real world perspective, the strategy clearly didn't pay off. Populations can really only support whoever is in front of them, and since Israel did its best to make sure Hamas was the dominant player in Gaza, well then Palestinians are going to support Hamas more than they would have if there were other viable options.
Sure. But, groups can moderate over time if given the incentives and prodding. There are no guarantees and it takes a really long time, but as I've mentioned previously, the ANA was able to moderate and become a viable government, as did many Irish nationalist groups who were unrepentant terrorists during the Troubles.
Looking for peace on your terms and not on terms likely to lead to a sustainable compromise isn't looking for peace. You can't tell me Israel was looking for peace in the two decades it was also occupying Gaza under martial law with no respect for Palestinian civil liberties.
Your argument ignores decades of history before the Second Intifada. Populations rarely wake up one day and decide they want to support bombings of civilians, whether directly or indirectly. Both intifadas happen within the context of decades of brutal occupation. That those bombings were wrong and unproductive doesn't change how we arrived at that juncture.