It's hard to really draw up the counterfactual but I'm not really sure that's the case. But there are many other players here besides just Israel that are helping to ensure that this conflict continues to fester, chiefly Iran.
I will point out the main reason it's hard to come up with, is the fact that American aid, weapons sales, and diplomatic support for Israel has been so constant and unchallenged over the past several decades that we don't have many good examples of what Israel would do without impunity.
I think there's an inclination on the Internet to lean toward one side or another, but just like with Democrats and Republicans, at least in my view, everyone sucks here.