Re: I reckon the proper term is 'institutional stupidity'
The advantage of file extensions is that they are easily portable across file systems (and comm networks), being in the file name. Any other solution is strongly tied to the file system, or at least the file structure, and it leads to portability issues. Mac and OS/2 had to add specific file/folders when writing to file systems not supporting their metadata, and those metadata could be easily lost when the file is copied without them.
It's also easier to create custom file types without complex procedures to register them somewhere - and requiring no external "registry" - but yes, it could lead to collisions.