Note that Cheddar isn't protected, but "West Country Farmhouse Cheddar" is.
My cynical take is that it doesn't have a more general designation because companies couldn't profit from Cheddar the way they do if it had to be produced in Cheddar Gorge.
Cheddar Gorge is a canyon, full of mobile hamburger stalls. There are no fields there, and no creameries. West Country Farmhouse Cheddar isn't produced in Cheddar Gorge. It doesn't even have to be produced in Somerset.
IIRC, there's only one cheese producer left in the actual village of Cheddar (others have moved to the surrounding areas), and they don't want to use a a PDO.
My cynical take is that it doesn't have a more general designation because companies couldn't profit from Cheddar the way they do if it had to be produced in Cheddar Gorge.