I'm not sure they do to remotely the extent that they would need to, for file extensions to make sense. I expect that, to the average (say) grandma, there are 3 or 4 kinds of files:
Video, Image, Audio, Other
The first three match human senses. The ear (audio), the eye (images), the combination with motion (video). People have understood those are inherently different things since their childhoods. If your grandam is more advanced, maybe she also understands documents (like PDF), that represent physical papers she has in her hand. In any case, those are all reflections of physical things she already understands, but that's about it. She probably doesn't even understand .exe given that every app she sees would have a shortcut icon.
Now you're proposing that jumping from that to .jpg/.png/.bmp/.tif/.jpeg/.tiff/.webp/.gif/.jp2/.mp3/.aac/.wav/.wma/.mp4/.mpg/.mov/etc. is a huge step? Given how confused I know even I have been about file types in the past and what they mean, I... don't agree.
And sorry, but security is secondary here. Usability comes first.