Thick budget OCBD?

I recently bought some Tyrwhitt OCBDs. Fits well, 100% cotton, but the (edit: lack of) thickness makes it feel cheap and a magnet for wrinkles. Honestly, not sure why these are recommended as much as they are.

The Ralph Lauren OCBDs I own don't have this same problem. Are there any other brands for low maintenance OCBDs? Less than $100 ideally.