On a Fedora 41 machine with a variety of DEs installed from Fedora
packaging (current GNOME, KDE, Xfce, MATE, Cinnamon), I have 650
.desktop files found in /usr/share/applications. Of these only 12 have
the execute bit set (all are KDE, but the vast majority of KDE-related
apps do not have it set, either). So the current common practice of
(system-wide) .desktop file installations would seem to be not to mark
them as executable. (Only one out of the 650 files in my installation
has a shebang line, and it is not marked executable!)