First of all I would remark that in move constructors or move assignment nothing should throw and there seems to be no need to this ever. The only thing which must be done in constructors/assignment operator is dealing with already allocated memory and pointers to them. Normally you should not call any other methods which can throw and your own moving inside your constructor/operator has no need to do so. But on the other hand a simple output of a debug message breaks this rule.
Optimization can be done in a some different ways. Automatically by the compiler and also by different implementations of code which uses your constructors and assignment operator. Take a look to the STL, there are some specializations for code which are different if you use exceptions or not which are implemented via type traits.
The compiler itself can optimize better while having the guarantee that any code did never throw. The compiler have a guaranteed call tree through your code which can be better inlined, compile time calculated or what so ever. The minimum optimization which can be done is to not store all the informations about the actual stack frame which is needed to handle the throw condition, like deallocation variables on the stack and other things.
There was also a question here: noexcept, stack unwinding and performance
Maybe your question is a duplicate to that?
A maybe helpful question related to this I found here: Are move constructors required to be noexcept?
This discuss the need of throwing in move operations.
What is the purpose of noexcept here?
At minimum saving some program space, which is not only relevant to move operations but for all functions. And if your class is used with STL containers or algorithms it can handled different which can result in better optimization if your STL implementation uses these informations. And maybe the compiler is able to get better general optimization because of a known call tree if all other things are compile time constant.