If you look at the source cited in the article, it's not a ban on 4 engine planes as a whole, it's a ban explicitly at Ben Gurion airport due to noise concerns, as it's surrounded by urban areas.
The residents of those areas have been complaining for many years about noise.
There are other airports in Israel that can accommodate large, 4 engine aircraft in terms of runway.
ETM and VDA come to mind but the former may not have the passenger handling capacity and the latter is now mostly closed to civilian aviation
It may be newer 2 engine aircraft are net better in "MPG" terms for freight, and pax loading for Israel doesn't demand 380/747 class craft. The jumbo 747 fleet is ageing, its old motor technology. Newer jumbos are exclusively freight.
Israel imposes far higher safety pre checks on pax. Maybe unit transfer costs in the system as a whole through their enhanced security simply scale better in lower units of pax as a single arrival?
Or maybe this reflects some local issues around noise, pollution, or when just some bizarre muscle flex by a specific segment of the political weirdness of the Knesset?
There are other airports in Israel that can accommodate large, 4 engine aircraft in terms of runway. ETM and VDA come to mind but the former may not have the passenger handling capacity and the latter is now mostly closed to civilian aviation