Armour is central to the battleship definition

Could a modern battleship be built at 50,000 to 60,000 tons with only splinter protection?

No; without armour intended to resist weapons comparable to its own, it would be a large cruiser rather than a battleship.

Displacement alone does not turn a ship into a battleship. Here, the type is defined by the ability to take fire on the scale of its own main armament and continue fighting. A 50,000- or 60,000-ton ship with only splinter protection may still be useful, but it lacks the defining protective system. Calling it a large cruiser preserves the distinction between carrying great firepower and being designed to exchange heavy blows.