I think this makes sense whenever there is a “most common” language in the area, but that isn’t always the case; for example, wiki recommends that border features have the “name” tag contain the names in all bordering languages: https://wiki.openstreetmap.org/wiki/Multilingual_names#Shared_boundary_features The Dead Sea is tagged this way.
I agree that we should encourage both name:he and name:ar to be set with the appropriate values on any feature that has a name at all. (Not just in Israel, by the way; some major streets in Berlin have name:he tags, and that’s absolutely fine.)
Aside: perhaps we should document our conventions on that wiki page too? So tourists who map in Israel know what our conventions are?