There were a thousand other paths they could have taken to "eradicate Hamas," but they chose the one that has no endgame, has thus far left Hamas in power, and inflicts nearly maximal human suffering. (They should have set up a humanitarian corridor that evacuates innocents to well-provisioned aid stations and temporary residences in the Negev.)
And, ultimately, if you're killing more women and children than enemy combatants, I think you're doing it very wrong.
Friendly reminder that the current Israeli government has for years supported Hamas, ignored the PLO and did it's best to isolate Palestinians in the west bank from those in Gaza.
Supporting and recognizing Hamas, allowing it to arm and find funds, by Israel was a deliberate move to avoid any two state solutions discussions.
Also, Israeli intelligence knew that October 7 was going to happen from one year prior (albeit they ignored the date) and did it's best to avoid preventing it.
Also no, US does not do anything when it comes to Israeli weapons killing countless civilians, no profit workers, doctors, nurses etc, neither in Gaza nor in other bordering countries.