That you presume (and even cherry pick and misinterpret) that Israelis don't care about the people of Gaza says a lot. If we didn't care about the people of Gaza, this whole story would have been over a good 20 years ago, certainly within two or three days max from the outbreak of the current war.

When Israelis say "human shields", it's not because Israelis are okay with Palestinians dying, it's because we know they're being deliberately put into the firing line by their "leaders" because we don't want to harm innocents. And most Palestinians - not all of them - appear to be okay with this because they've literally been brainwashed by the Iranians over the course of generations into believing that being martyrs is the best they can hope for.

Destroying Hamas means destroying their ability to hurt us further, right now. Resolving the fundamental ideological issues and finding a way to live in peace with our neighbors is secondary, but no less important, and it's something being discussed in all sectors of Israeli society. It looks like as soon as things calm down, Netanyahu and his cronies are going to become irrelevant, and I hope we'll all learn important lessons about just how toxic and misinformed our media, both mainstream and social, have become.