I think that used to be pretty common "back in the day". As well as putting on a beard protector, a piece of fabric over the top edge (usually a thin muslin, to protect the fabric from the coarse beard/grease and not the beard from the fabric!).
The only real downside is it definitely makes the quilt directional, but sometimes that can be a good thing. You ever have the does the quilt go this way or that way on an almost square one?