//What's the point in staying open with no customers?//
Exactly. It was a ridiculous request on two fronts:
1. If a pub is open people will go into it.
2. As you say, why run a pub (heat, light, staff, costs etc.) if you've no customers. You'd do better to close voluntarily (perhaps that's what the PM was hoping for to save the taxpayer having to pay the wages of those displaced).