Israel's concern is war material aid and fighters crossing the border - both ways. They are serious at the moment about ending Hamas as a functional org and don't want individuals slipping the area.
I think there's a possibility to establish a trans-loading operation: Aid gets delivered thru Egypt, offloaded literally at the border, inspected, picked up, and crossed into Gaza. But the schedule to establish this is so far behind the curve, that.....I don't know. That's the big question: we all know what's immediately coming, but its what comes next that is just a black hole right now.
Egypt is supremely suspicious of Israel wanting to push (previously), force (currently) as many Gaza Palestinians into the Sinai as possible. I would think they would also be wary of creating further conditions at the border enabling a bum rush out of Gaza, overwhelming Egyptian security/AF.