Roots, Mulch and No Dig

I practice a sort of No Dig, forking out mole or vole runs as needed, which can sometimes be a whole bed, but in general just mulching with compost and grass clippings to keep down the weeds and put goodness back in.
However, I've always left that year's root patch unmulched not wanting to add too much goodness, but this leaves the soil exposed to the heat and rain as well as passing weed seeds. Now I'm thinking I should be mulching here, too. 
I only grow parsnips and carrots, neither particularly successfully, in the roots rotation.
Any thoughts?