I think this is slightly too dismissive of Israel's own agency in the conflict. I do think that destabilizing the Middle East in this fashion (not just spreading chaos and death in Iraq and Syria but it actually meaningfully impacting both Israel, Saudi Arabia, and the other monarchies) isn't in America's best interests. I think if you asked the top people in the deep state "If you had a choice between having a war between Israel and Hezbollah and not having that war, which would you pick?" then they'd answer 'not having a war'. America has actively benefitted from the status quo over the last century, has shaped the region as best it could to align with its geopolitical interests, and now this genocide and war threatens to upset that project. The endangerment of various private military corporations rampaging through the Middle East is fairly unimportant, they're just there to take the losses and do the dirtiest work. Losing Israel, or it even being massively weakened, is actually catastrophic, but also fairly possible to achieve because Israel is tiny and surrounded by very angry regional forces. The entire "deterrence" paradigm was established specifically so this exact situation would not be allowed to occur. Israel getting caught up in an existential war should not have been allowed to happen. That this situation has now occurred is a blow to the US.

The issue is that there's no interest, or at least concentrated will, inside the US government to tell Israel that they're endangering their imperialist project in the Middle East. It's at least partially sunk cost, and at least partially that if Israel is forced to back down, then the deterrence paradigm is still shattered, which means that another war in 2, 5, 10 years could happen. If Biden called Israel tomorrow and was like "That's enough. We are stopping all military and financial aid unless you end the siege of Gaza and sign a deal with the Resistance," then even if Israel did that, then Hezbollah and Hamas and everybody else isn't going to go "Well, all in a year's work! Time to disband and stop fighting Israel! They might be in a historically weak position, but we got the deal we wanted!" They're going to rebuild and prepare for the next round, and with Iran strengthening due to the help of Russia and a rapidly ascending China, and the US failing to maintain industrial production of key military equipment and instead burning trillions on F-35s, the next war will be even more lopsided against Israel.

So there's no way out. Iran and friends have manuevered the empire into a trap, just as Russia did in Ukraine. Just as the US has/will find it extraordinarily difficult to surrender in Ukraine because of all the implications of that move and so feel compelled to keep fighting even if their analysts know that they're doomed, the same situation is occurring in Israel. If they keep fighting, it means the further destruction of the imperial architecture that took decades to build. If they give up, they've gained nothing, they've lost a lot (of both physical military equipment and soft power around the world), they've been dealt a big psychological blow, and they know that the next round of fighting (a cold or hot war) will be even worse. Europe being substantially weakened as an imperial rival is the only significant achievement that they've managed. It's a pretty good one, but does that make up for everything else? Europe was already stagnating for years and years before the Ukraine War began.