I am about to put less knobbly tyres on my CX, ready for summer riding on our disused railway line nearby (turned into a cycle path/foot path/bridleway. I love my roadie but I also love my CX bike as it's such a good all rounder. I commute on it, whizz to the shops on it or just go out for a play on it.
With the right tyres on a CX, there is not reason that you shouldn't ride a coast to coast on it.