For example how would you implement std::function without overloaded operator()?
Also lambdas are defined in term of structs with overloaded operator ().
Without overloading, the standard could still ad-hoc define the specifications of lambdas and std::function, std:: ref, etc, but the language would be worse off.
To be mildly pedantic, printing in a destructor is horrible practice because stdout/stderr might be pipes or sockets and writing might fail. It's a really bad idea to do anything in a destructor that effects anything but the class being destroyed for those reasons, and when you get an error, it shows up as an opaque exception or trace or hang at the end of a scope instead of where it actually mattered.