Given Hamas’ record in the prompt and careful delivery of aid, giving this job to some other organisation might produce a better outcome for the people of Gaza.
Mahmoud Abbas says (of course) that the Palestinian Authority should be in charge of relief efforts. The PA has a history of indolence and corruption, but at least they are not formally committed to the destruction of all Jews, everywhere. So there is some realistic prospect for peace between Israel and a Palestinian State lead by the PA.
But there has been a serious decline in the already poor relationship between Hamas and the PA, with reports over a hundred Fatah members in Gaza have been murdered by Hamas in the last few weeks, many of them tortured to death, and at least three having had their eyes gouged out. This makes it seem likely that giving the PA responsibility for aid distribution in Gaza would lead to renewed fighting, with the potential for much greater loss of life than in Hamas’ conflict with Israel.
Egypt or Jordan are not likely to want to take responsibility for aid distribution, when this would expose them to violent retribution from Hamas, and by proxy Iran. Much as I hate to say it, this may be a time when direct UN responsibility for the distribution of aid is the only option likely to produce positive outcomes for the people of Gaza.
More on aid from Israel to Gaza: “More than 37,000 tons of staple foodstuff and emergency medical supplies entered the Gaza Strip through one Israeli crossing from the time Israel began its military offensive until it declared a unilateral cease-fire on January 17.”