It seems from now to Wrestlemania (if my predictions are correct) that Ambrose will be booked in programs that don't revolve around the US Championship, as he is currently focused on destroying Punk, then out to win the Royal Rumble (which will cause a stir between all three members I'm sure, continuing the march towards their breakup), then probably crossing paths with the Wyatts that pits both teams against each other at Mania, leading to The Shield break-up after Mania is over.
Point is, he doesn't need the title. Arguably, he never really did but it at least made some sense at first because the Shield winning a bunch of gold was a way of further demonstrating their dominance but at this point, putting the US Title on someone else gives others an interesting program to work while Ambrose will continue to take part in relevant feuds without the title regardless. Have Punk cost him the strap next Monday on Raw as a way of Punk getting a big one over the group, causing them to lose the last championship that they currently possess. .