A cheap operation is still infinitely more costly than no operation at all though. And not everything is on a local SSD, even just with a NAS, not to mention FTP, I really wouldn't want there to be no file extensions.
How would webdev look like? At first the HTML goes into "document", the style into "style", and before you know it, you're re-inventing extensions as prefixes or suffixes anyway, and I prefer users.sqlite to users_db. I honestly don't even see a problem to solve, so even the "cheapest" solution seems needlessly costly to me.