lsrael is, in a sense, stuck in a quagmire, it cannot--probably evident since 73, certainly evident today--acheive a decisive military victory over its foes, but it also cannot conceive of an alternative strategy which all sides--including the Palestinians--can live with, so it is doomed to repeat the same inadequate moves from its playbook, to continued stalemate at best.
They're absolutely stuck in a quagmire, largely of their own making. It's not that they can't achieve decisive military victory, it's that military victory doesn't solve the issue of Palestinian disenfranchisement as it did with the Arab states. it's basic Clausewitz stuff - a military victory is useful in so far as it furthers or achieves a political goal. Look at how many people, including Israelis, have been asking what Israel's endgame in this invasion is beyond destruction. it's a problem that doesn't have a military solution. they cannot, as you say, simply kill their way out of it.
The Israeli RW has a fantasy of expelling the Palestinians and annexing the territories - normally just the WB bc no one actually wants Gaza, but the war has definitely added Gaza in a "we're there, might as well" way - but it's just that, a fantasy. even the U.S. won't stand by for that. the one line Blinken and Biden have consistently held is pushing back on any reoccupation of Gaza, let alone new settlements. So they can't ethnically cleanse their way out of it either. all the extremist settler bullshit is an attempt to do so bit by bit.
To step back a bit historically, force vs rapprochement is a debate within Zionism that predates the founding of Israel. The middle ground was traditionally pragmatic realism based on how Israeli leadership viewed the situation at a given time. I.e. in the triumphal post-67 conceptzia glow they were unwilling to trade land for peace with the Arab states. After 73, they were.
The occupations - more broadly Israel's relationship with Palestinian liberation, but specifically the occupations - begin a departure from any kind of pragmatism. Even leaving aside their poisonous effect Israeli society, which can't be overstated, they haven't made Israelis safer. The settlements, brutality and general illegality of the occupations are a huge embarrassment to, and a geopolitical strategic headache for, the U.S. and most importantly, the occupations have only strengthened the Palestinian desire for liberation.
I've said, you said it, a thousand people have said it elsewhere: Oct 7 ended the fantasy of endless occupation at acceptable cost. It was a specific illusion of Netanyahu and his allies, tho it must be said, accepted almost without criticism by the opposition as well as the large majority of Israeli society. the only solution is a Palestinian state based on the 1967 borders, probably with some land swaps, and some kind of transition under an international peacekeeping force. that's always been the only real solution. everything else will just be doubling down on the quagmire.