Yeah; the difference between Box and a regular object would be the object is on the heap instead of the stack (just like it is with uniqueptr). I say its a footgun to have an implicitly copyable uniqueptr because a reasonable use of using the heap that way is for stuff too big to go on the stack, and too big would also mean you also don't want to treat copy as a trivial operation.
Often classes don't have a copy constructor if it's expensive to copy for the same reason though, which means they wouldn't be eligible for the proposed Box behavior either though so maybe its not a real problem.