This is to a large part to give Egypt plausible deniability. They don’t want to deal with Gaza, refugees, or a humanitarian crisis, but also don’t want the political fallout of taking action like the Israelis do.
On the contrary, I believe Israel would be delighted. It would lessen the humanitarian burden on them, and force Egypt to deal with the Hamas problem more directly. It will never happen, though. No Arab country will "throw the gates wide open" for Palestinians. They have done so before, several times, and it went very badly.
The Israeli openly proposed for the Gaza Palestinians to move to Egypt (effectively ethnic cleansing Gaza, their obvious goal), not that long after 7.10.
Egypt said 'HELL NO', first, because they don't want to deal with Palestinians (both political and economic nightmare), and second because it would have been viewed as ceding to Israelis and helping them cleanse Gaza, which would be highly unpopular among their population.
Israel would object to aid and weapons flows into Gaza. It would be fine with Gazans leaving the Strip. The problem is there are currently zero takers globally for a significant Palestinian refugee population, in part, as other comments have mentioned, due to the history of Palestinian refugee populations in the Middle East. (To my knowledge, Palestinian Americans have been fine and productive members of society.)
More like refugees flowing out, which Egypt doesn't want to deal with.
The Palestinians didn't help their cause with Yasser Arafat's Black September uprising in Jordan. Then they topped that up with strong support for Saddam when he invaded Kuwait. Like the ones in Kuwait were literally betraying Kuwaitis to the Iraqi troops.
Oh, and did I forget Lebanon? They literally fomented the civil war.