IMO they're trying to make situation so dire that other parties capituate to resettling Gaza. The intention is expulsion not nessicarily genocide, but that doesn't mean current actions and rhetoric, even if flippant, can't be used against Israel in international court / opinion. I'm not saying what Israel is doing IS genocide, but there's probably enough bits and pieces for interested parties to weave genocide narrative, especially the longer war drags out and more dire Gaza situation becomes.
> removing this organization is in the best interest of both people
I don't disagree, for short term. But without Israel expressing interest or some effort at making 2 state solution work, it's kicking can down the road. The fundmental problem, as seen with Hamas, and Houthis is technology proliferation of not garbage tier weapons is making Israel's lack of strategic depth less and less defendable by the day. General arab acrimony is not going to go away after this, and US+Israel can only maintain their military advantage for so long before rest of region catches up or surpasses due to sheer scale. Each generation is more capable than the last and ultimately there's 400 muslims in MENA vs 10m jews in Israel on sacred lands. And this war is just setting up for blowback down the road, especially as US FP will likely change as new gens are much more sympathetic to palestine.
As for Palestinians, they will not forget this. Hamas/resistance will come back in one way or another. The other reality, which makes this problem intractable is poor Gaza with 90% literacy rate and limited access to modern tech / resources was enough to overwhelm Israel on Oct 7th. Israel can barely live with a semi capable Gaza, and definitely can't live with a capable (free) one. Given how weapons are proliferating, Hamas rockets likely a few iterations from taking out existential Israeli strategic targets like desalination plants. There isn't isn't enough geographic buffer for both people to exist on the same land, not without one permenantly keeping other down. Hence IMO Israel will try to make Palestinians disappear from Gaza, one way or another.