It is unclear why Egypt would risk jeopardizing a cease-fire that US Secretary of State Antony Blinken called "extraordinarily generous on the part of Israel." Though Egypt will likely remain as a mediator, Qatar will certainly play a larger role in the next round of talks, but it will also depend on whether Hamas wants to make concessions or not.
Egyptian intelligence toyed with the cease-fire proposal in a desperate attempt to end or shorten the war, as it has created negative perceptions of Egypt's government. It's to be expected that Egyptian officials must publicly decry Israel's legitimate security operations, but, behind closed doors, there have been no significant changes to the Egyptian-Israeli relationship.
It is a shame that the US media and political apparatus constantly feel the need to cover Israel's intransigence at every turn. After seven months of a grinding campaign of destruction, displacement, and famine, it should be clear that Israel is not interested in ending the war. There was nothing in Hamas' proposal that is surprising. Netanyahu simply needs an excuse to extend the war and his political career, and the Americans are helping him.