There's only 4 possible outcomes to the entire issue:
Two states
Annexation
Status quo, indefinitely
Ethnic cleansing
Israel will never let #2 happen, for a bunch of obvious reasons that have already been discussed in this thread. Not worth talking about.
Only the most unhinged right-wing voices in Israel and the US even bring up #4. Also not a whole lot to say there.
Israel clearly prefers #3 to #1. I think that's for two main reasons: 1) in order for two states to happen, they'd have to either forcibly remove their own citizens from big chunks of the West Bank (politically disastrous), or they'd have to make painful land concessions to the Palestinians (...politically disastrous), and 2) they believe it enhances their security situation.
The first reason is a problem entirely of their own creation. I don't have a lot of sympathy. The international community, including their own closest allies, has warned them again and again and again that West Bank settlements are a horrible idea, and they just don't give a fuck. The fact that they would have to eat that shit sandwich should not be a valid excuse.
Their second reason for preferring the status quo (enhanced security) is a valid reason, but it's also a miscalculation. The status quo costs them their relationship with the Arab world, it harms their standing around the world to varying degrees, and it radicalizes the Palestinian population. It's also contrary to Israel's foundation as a democratic country, for good measure.
You say that the Palestinians want the extermination of Israel/the Jews. Hamas clearly wants that. I can buy that the average Palestinian man on the street might say that if a reporter sticks a microphone in his face. But IMO most people, if left alone, just want to kinda...live their lives. Still to this day, a disturbingly large percentage of Americans subscribe to the preposterous belief that the 2020 election was stolen. But how many actually attacked the capitol? A few hundred? The rest are just...at work. Living their lives, posting garbage on Facebook.
Hamas is a terrorist organization, full stop. It should absolutely be dealt with as such. But so was Al Qaeda, and we never intended to take control of Afghanistan forever. So was ISIS, and we never tried to take control of Syria. Israel has the ability (and the right) to secure its border with a hypothetical Palestinian state. We're not talking about the US-Canada border, here. If Hamas acts up, bitch slap them. Hell, invade and take them out, just like we did with Afghanistan and Al Qaeda. We'd cover for them at the Security Council, no sweat.