A lot of constants are known at compile time and constexpr solves a lot of problems. However, you do not need constexpr to solve your example- this is still a compile error:

void iter(std::vector<int>& vec) {

     auto& vec_size = vec.size();

     vec_size += 10; //compile error 

}

There are many ways of forcing compile errors for mutexes that people have built, but they all come with their own trade-offs.

I've not encountered a problem where I specifically needed "non-ref-counted shared references while statically avoiding dangling pointers", so I'm not an expert on it.