Part of the reason there would be as many if not more wars than OTL. This area would be contested between the Palestinians, Jordan and Egypt at the very least.
They don't call this a bit of a bad neighborhood for nothing...![]()
Syria might stake a claim if opportunity arises.
However, this raises the question of WHY exactly Israel is not there ITTL.
If the POD is "no meaningful Zionism arising" (dunno, kill Theodor Herzl) then there would be no such a thing as Mandate of Palestine to begin with, not to mention Jordan. The whole diplomacy around the Arab Revolt is different and you might even get the united Arab State promised to the Hashimites, albeit in a reduced form (no way it would include Lebanon). There will be conflicts for sure, but with differents borders and different players. No Balfour Declaration could bring to a similar scenario, though by that point, Zionism would be at least a minor local factor already.
If the POD is "Israel is defeated in 1948" you have more or less OTL outline of borders except in Mandate of Palestine. By this point, many Palestinians might or might not be willing to be rule by either Jordan or possibly Syria, it depends to many factors including how the war had played out. You'd have also some problems regarding what to do with 600 thousand odd Jews immigrated there, some of them with horrible histories from Europe.
Jordanian claim is going to be the more solid, but then, Jordan might reconsider her willingness to get the whole mess and let Egypt and Syria take a share of the fruits of the victory, out of "arab solidarity" (read: we're not going to afford tidying this disaster alone).
In any case, the Egyptian monarchy is more solid and stronger. This butterflies the whole ideological confrontations that ensued, at least as long as the fifties go.
Will Britain do something stupid in Suez ITTL without Israel as a willing local proxy?