It's not that black and white. If the mission was just, "Kill fifty thousand members of a group you consider a terrorist group located in open terrain in 1980s-style camps in North Africa," then Bibi would have dialed up Biden and asked, "Do you mind?" Biden would have said, "Sure, I could use a political win back home right now," and that would be the end of this.
Unfortunately, the Israel-Palestine issue has a messy history, Hamas is located in very problematic terrain, they have hostages, they have civilian shields and they aren't stupid. Counter-insurgency is always a mess, it's much more difficult in urban (or mountainous/jungle) terrain and collateral damage just breeds more terrorists, as
@Mutzo Nutzo is saying. By the usual 10:1 rule, killing ten thousand Gazan civilians means Israel has only accomplished doubling the present size of Hamas in a few years,
even if they kill every current member of Hamas and never kill another civilian from this moment.
The problem here isn't just that what the Israeli government is doing is cruel beyond human imagining. It's also self-defeating, and not just on the terrorism side of the fence. It's costing Israel in Western media. CNN was unequivocally pro-Israel when compared to other mainstream US outlets from October 7 forward. Now, they're running things that only received media oxygen in other outlets. The slideshow at the top of NBC's page is entirely comprised of rubble and Gazan suffering, and they started out charting a middle ground. The NYT and WaPo are starting to join that party. Sooner or later, ABC and CBS are likely to follow, and MSNBC has shifted from pro-Israel to avoiding the issue.
Bibi couldn't ask for better occupants of the Oval Office and State chairs right now, in the sense that they're among the last people in American politics likely to turn on him, but the media pressure is now mounting. The unfiltered stuff people get from places like Instagram and Twitter is (and already was) incredibly ugly, which is why young people have already turned on Israel here. The worst part is that
all of this was entirely predictable from the outset.