A trivial suggestion…
When saving a script, make the “Hide extension” option persist, retaining the setting from the previous save.
I’m forever changing it.
I don’t know if this suits you, but if you go to Finder Preferences and check Show all filename extensions, the Hide extension option disappears altogether.
Show all filename extensions
Thanks for the suggestion, but that would achieve the opposite of my goal – I prefer not to see file extensions.