It's clear that Israel intends to dramatically change Gaza so Hamas (or any other radical group) can no longer threaten its people. So how might they do this? Here's one scenario.
Israel wants to wipe out Hamas and also depopulate Gaza so it can never again be a seed bed for terrorism. But how can they do this without killing most of the people there, which is clearly unacceptable? Start with the fact that Israel has already prepared to cut Gaza in two, with the demarkation point being the Wadi Gaza in the middle of the strip. All the land north of the Wadi, including Gaza City has been marked for the initial clearing operation and more than half its population has already left. The other half will be driven south or killed along with Hamas leadership and fighters.
So what will the Israelis do about the southern half of Gaza? My guess is they won't have to do much. Why? Because of the relentless population pressure caused by jamming the 1.1 million or so Palestinians from the north end of the strip into the south where there isn't enough infrastructure to support them. Over time, more and more of them will figure out ways to escape, either by getting over/through the fence separating them from the Egyptian Sinai, or in small boats to either Sinai or Lebanon. The one thing the Israelis will prevent is any of them getting into Israel itself or the West Bank.
How many Palestinians will be left in Gaza after that? Who knows? But it will certainly be far less than there are now.
Israel will continue to occupy what's left of Northern Gaza, holding it until there's a broader peace agreement. But it will be a virtual desert. Picture Stalingrad after it fell.
None of the above is intended to be judgmental, just a possible (or even likely) outcome.

…would be for Israel to annex the Gaza Strip entirely. That way their only border concern in the region would be with Egypt. The US and Israel should pressure Lebanon and Egypt to take in the refugees. If Islamic terrorists see that their actions directly results in Israel expanding their borders, then that alone should give them the incentive to stop engaging in terrorism.

Not to mention that annexation would kill any effort to normalize relations with the broader Arab world, which is clearly to Israel's benefit.
Do you really think Israel would be better off if the Saudis and others (like the Jordanians, etc.) renounced the Abraham Accords (practically the only foreign policy victory Trump had)?
No, Gaza is unimportant if it's no longer the home of Hamas.
The real question is, to what extent is Israel still committed to a two-state solution? The answer is Netanyahu and his cronies are not. They are trying to create "facts on the ground" that will make a Palestinian state impossible. And that is a formula for war everlasting.
Not to mention that annexation would do the opposite of what you say. It would actually spur terrorism. Consider this: since 1948 the Israelis have been kicking the shit out of the Arabs and annexing places like the Golan Heights. And that has certainly not stopped terrorism.

If the annexation of Gaza would further enflame the situation, it’s not worth doing, but it should be a long term goal. Quite frankly, I’ve always thought a 2 state solution was not really a feasible option. The Palestinians can go to any of the neighboring Arabic states. Israel ought to just take the West Bank entirely. How practical an option that is, I don’t know.

In 1948 they were given their own state, as were the Jews. The Palestinians rejected this, along with all the Arab states and went to war with Israel with the stated goal of driving the Jews into the sea. They lost. Since then most Palestinians (except those who stayed in Israel and are citizens) have lived in refugee camps. They have been kept there by the Arab states who used them as a political football in the ongoing war with Israel. Now there is only the solution of a Palestinian state. Without one, the Palestinians have no reason to stop using terrorism. The problem is that Israel has made it almost impossible for a viable Palestinian state by continually encroaching on Palestinian lands in the West Bank. This has been pushed by Netanyahu and his religious right cronies. It is almost too late.

…I was largely unaware of the main points of the history until recently. It’s a very long history, and that alone is pretty overwhelming. The Roman Empire was significant, but their actions don’t play much into modern conflicts. But it certainly does here. My current understanding of things is that there’s really no such thing as “Palestinians”. It’s just a concept created by the Romans to punish the Jews for a rebellion that pissed them off. My understanding of the “Palestinians” in Gaza are mostly just displaced Egyptians. It seems to me that the most humane thing the US can do is put pressure on Egypt to open their border to Gaza and let their own people in. After this attack, there’s no reason why the Gaza strip should exist at all. Israeli national security would demand it’s total annexation.

Hamas is the offspring of Egypt's Muslim Brotherhood, which is illegal in Egypt and most of its leaders languish in Egyptian jails. I don't think you'll see them welcoming Palestinians into their midst.

Ah, I didn’t realize this about Hamas. Isn’t the Muslim Brotherhood the crazy fucks to assassinated Sadat?  

But tell me, Willy, how the heck do you know that "Hamas has the support of a lot of the people in Gaza?" I'm not saying they do or they don't, but the last (and only) election that Hamas won was in 2006. They have not permitted elections since while exploiting the ordinary people of Gaza and running a dictatorship.
Hamas KNEW Israel would act as it has. They provoked this and deserve what they get. What's important is for Israel to at least appear to be trying to minimize innocent losses and have some plan for what comes next.

Hamas got 44.4% of the vote.
Fatah got 41.4%.
My guess is Hamas would get less today.

Countries that have been somewhat supportive of Hamas should be taking in the refugees created as a result of the Hamas attack. Send them to Qatar, Turkey, Syria and Iran.

for its total mis-understanding of history and sheer obtuseness.
First of all, go back to 1948. Hundreds of thousands of Palestinians were made refugees. Did any Arab state take them in? Nope. They penned them up in refugee camps and refused to let them assimilate. They certainly won't do it now, despite ChicKenShit's naive hopes. Egypt won't let them in either because it hates Hamas as the spawn of the Muslim Brotherhood, which has been Egypt's scourge.
As for what the majority of Gazans think, I have no idea. I simply suggested no one else did either.
Especially not ChicKenShit, our least reasonable and least intelligent poster. Except for durranDolt, the Piñata-Boy Pussy and snowflake.

Because Palestinian children are groomed in school from an early age to be Jew-haters, much the same way American children are groomed to be sexualized at an early age.  If these neighboring countries take them in, they just become a platform for future attacks on Israel, and these two countries want none of that because they have been at peace with their neighbor for many years.    

No, Egypt and Jordan do not want them. And have been rejecting them since 1948. And then you go off on a side track with your fantasy about American kids who "are groomed." At least you didn't say they were being groomed to be gender-fluid. I guess that's progress.
As for Palestinians who might move to Egypt or Jordan becoming "a platform for future attacks on Israel," what do you think they are in Gaza? Were you asleep when thousands of them breached the border fence and murdered around 1500 Israelis? What will stop them is finally getting their own state, the creation of which is less likely than ever.