It has, by almost any measure, been a depressing week. Make that, a depressing few years. Make that – well, ever since Hamas was voted in, or since Gaza was given to the Palestinians and they scorched the earth on which crops had been planted to give them an agricultural industry and then they looked to scorch Israel.

Look, I normally write about the arts. Politics isn’t my specialist area. But I take a keen interest in Israel’s affairs and I, like most Israelis, desperately want to see peace in the world’s only Jewish state but  – like most Israelis – was dismayed by what happened after the Gaza experiment. Once upon a time peace seemed tantalisingly near. Today we – Israelis, Jews, all who seek peace – seem bereft of ideas.

So fresh thinking is called for. And something radical has occurred to me, something that as far as I know nobody has yet suggested, at least not publicly.

Give Gaza to Egypt. This notion, which in itself would of course take much strategising (and not a little pressure from the US) between all the involved parties, would once have been unthinkable. Israel’s sworn enemies pre-Sadat and the peace treaty have attacked Israel on multiple occasions. It is still counter-intuitive, to say the least. The Egyptian public have long been hostile, often virulently so, to their Jewish neighbours. We have only just seen the removal of a Muslim Brotherhood government, ideological first cousins to Hamas, and the Sinai remains a problem area. Added to which, for Egypt as for other Arab states, the Palestinians have long been an invaluable propaganda tool to distract their disenfranchised people from the dictatorship at home.

And yet. Consider the following. Egypt has been a pretty good neighbour, reliable in security cooperation (including in the security buffer zone of the Sinai, where they have been careful to ask permission when they have needed to send in troops to capture militants). They are a dependable partner of the US, Israel’s closest and most powerful friend and likewise Egypt’s benefactor. They – meaning the Egyptian army, which effectively, and now actually, runs the country – seem to realise, in short, that doing business with Israel and the West is in their best interests.

So why would they want Gaza? Why ever would they want to burden themselves with that political headache? Headache? Migraine.

A few reasons. In recent years, Egypt’s de facto position as the natural leader of the Muslim world (as the Middle East’s most populous country) has been seriously challenged by the overweening ambitions of Iran and its tempestuous strategic ally Syria, and the machinations of Erdogan’s Turkey. Being seen to swoop in as the great benefactors and protectors in the unifying Arab cause of the Palestinians would in one dramatic gesture restore them unassailably to the top of that particular pecking order. In any case, the potency of the Palestinians as a way of distracting their own populace has dulled with the Arab Spring. It didn’t help the ousted Mohammed Morsi, who made great play of the issue, and it has in fact barely been a factor in the various recent uprisings and revolutions. So why not turn it on its head and try a fresh approach?

Next, Hamas is the hated Muslim Brotherhood on Egypt’s doorstep (they share a border with Gaza). Removing them from Gaza would help complete a process of wiping that organisation from every nook and cranny in and around Egypt that the current rulers there have undertaken with relish.

And it would deal a blow to Egypt’s principal regional rival and ancient tribal enemy, Iran – who have poured effort and money (and arms) into making the Palestinian issue one of their main rallying calls. Finally, it would play well with America and the West, doubtless leading to an enhanced diplomatic role and, let’s face it, more cool guns and money and stuff for the Egyptian army. For all of these reasons and a few more, it would make sense for Egypt.

Why would it make sense for Israel? Well, unless you believe that Israel should reoccupy the strip – which to some of us would likely be a nightmare scenario leading to street war, atrocities, and a dehumanising, no-escape, no-end conflict – this would be the least-worst option. Israel cannot keep Gaza. That horse has bolted. And the demographics of the place mean that they wouldn’t want to.

So who gets to have it? Hamas? Be serious. The Palestinian Authority? Maybe, but last time they didn’t prove that they could keep it from the clutches of extremist groups. There are also other reasons to mistrust the PA – for now. So who is left? The UN? They couldn’t even keep the Lebanese border quiet. America? Desperately unpopular with the Arabs, for all President Obama’s conciliatory gestures.

But Egypt makes sense. Israel already shares a border with them, and it has been seen to work for decades now. They could if they so wished genuinely help forge a society that didn’t demonise Israelis and Jews (unlikely, I know) and they are powerful enough to start to normalise relations. Wiping out Hamas would be order of business number one for them. More practically, perhaps, they are a large state with an army so there would be no need for Gaza to be militarised. Neither would it need an airport (both red lines for Netanyahu and Israel) with the crossing to Egypt and its transport hubs opened.

And, let’s face it, if there was a radical change of regime or thinking on the Egyptian side and missiles started firing again, Israel would have a country to attack, not an over-populated enclave where civilians get hurt and the media has a field day. Gaza, under Egyptian rule or mandate, attacks Israel? Fine, Israel can send the full force of its weaponry to clinically strike important assets deep into Egypt itself. Which should help to convince them that the cost of stirring up trouble in Gaza outweighs any propaganda benefits.

It makes sense. At least it’s worth investigating. We gave them back the Sinai. Giving them a little more could actually be the best favour we could do for ourselves. And for the population of Gaza itself.