I agree entirely with your assessment.
My phrasing was specific to the Oct 7 attack because that event was the provication of the current conflict.
Despite policies like "mowing the grass" being catalysts for the Oct 7 attack, my point is that Isreal has stated a clear objective: elimination of Hamas. Their terror tactics are described in the Wiki link you provided appear to be supportive of that goal too.
Hamas has also stated a clear objective so far as I know: destruction of the Isreal state (potentially also of all Jews, but let's give them the benefit of the doubt and say just the state).
I'm undereducated on the issue, but to me it seems that there is no reconciliation of these goals. They are not simultaneously achievable.
My estimate is this conflict could end today if Hamas conceded. What would become of Palestine is a different matter. Their current authority, the PA, seems to have a policy of paying familes for insurgent deaths. Isreal probably won't want them running the show,and they definitely won't want Hamas running it. Other bordering countries like Jordan and Egypt seem to want nothing to do with Palestinians. The Palestinian children appear to be raised to hate Isrealies and are taught to murder, perhaps justifiably (and maybe this is wrong and only propaganda).
I want this fixed, and I can see a path forward where Palestine embraces sovereignty and becomes a mecca of the world by operating as a tax haven for businesses. But in order to do that they need to determine their goal is peace, and ally with other countries for protection against Isrealie aggression. But that is a hard path forward when starting at current state, including the world view held by Palestinians.
And maybe I'm entirely wrong in this post. But my GP post was specific to my perceived, orthogonal objectives of both sides.