Just so we are all on the same page…
  1. The Finder .plist has only a single parameter about showing extensions and only two possible values Yes and No.
    • Deleting that property list and allowing it to be recreated should have cleared up any damage there
    • the default value is NO
    • in any case setting that value to YES (checking the box in Finder > Preferences > Advanced) would force all of the extensions on your system to show not just some of them.
  2. If either Finder or Get Info is set to show the extension — the extension WILL show. (I just tested that out to satisfy my own curiosity.)
THEREFORE IF
  • Finder > Preferences > Advanced > Show all filename extensions is UNchecked and…
  • in Get Info in those files "Hide extension" IS checked and…
  • any of the extensions are showing or…
  • some but not all file extensions are showing…
  • THEN it would appear likely the problem is in the OS itself.
For what it is worth, I learned long ago when working in tech support that a problem like that can take forever to troubleshoot and solve but it can almost always be "fixed" by reinstalling the OS which at best takes less than an hour and is dead simple to do. Just boot from the Recovery Drive and run the installer.

It it were me, while I was booted from the Recovery Drive, I would run Disk Utility > First Aid on the hard drive before reinstalling the OS, just to be sure there isn't an underlying problem there.

NOTE: Unless there are overriding reasons for staying permanantly with Sierra, this would be a good time to upgrade to High Sierra. (Even Artie finally gave in and upgraded laugh )

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein