The only thing I'd worry about with used cotton sheets is rot from exposure to body oils. There is something about my DH's body chemistry - our fitted sheets become rotted and fragile on his side of the bed after just a few years and eventually start literally falling apart in the middle. I don't see the problem as much on top sheets but it makes me not want to use our old sheets for quilting, other than maybe for foundation piecing.
But new sheets - I don't see any reason at all why they wouldn't work. Just watch out for cheap poly blends that might pill up with use.