A modern 16-inch autoloader needs a much larger ship

Could a modern warship use a single-barrel 16-inch autoloading gun instead of an eight-inch weapon?

Not on most current ships, because the gun and its support systems would require substantially more space than their hulls provide.

A single-barrel 16-inch autoloading gun would consume a great deal of space. Contemporary surface combatants are not generally large enough to accommodate such a weapon and its supporting machinery. The apparent simplicity of one barrel does not remove the ship-scale penalty.