But... But it takes less time to fold a fitted sheet than a regular one?

A regular one you have to manually square up all the corners with each fold.

Fitted though, slam that thing in half, stick your hand in a corner (like a mitten) and stick the nearest corner over the top. Do the same on the other side, and then flip two of the corners into the other two. Ignore the bunchy bit around half of the sheet, and pretend the corner of the mitten (where all four fitted corners are now stacked on top of each other) is the"real" corner. Fold once or twice more on top of itself and you're done.

And significantly faster than folding non-fitted sheets, because you don't have to find the corners and line them up.