That's a fascinating topic, thanks for bringing it up.
I often use file extensions as visual helpers or when scripting to filter files by extension.

They are definitely useful for recognition by other programs, such as text editors for instance.
More than this, I wrote about default programs (and here) and the extension is definitely used to discover the mime type of the file, and thus the default program to use to open them.

It doesn't end there even, on Linux you can use the binfmt functionality with the E type format to say that the executable is chosen based on the filename extension. So you can, in theory, recreate the Windows behavior on Linux. If I recall properly, that's how WSL (Windows Subsystem for Linux) implements being able to call .exe like explorer.exe.