std::enable_shared_from_this, non-virtual destructor and public inheritance

The std::enable_shared_from_this class is a (template) mixin, recommended for use to enable creating shared pointers from a given object (or its address), which all have common ownership of the object.

The thing is, that if you have an class T which:

1. Has virtual methods
2. inherits from std::enable_shared_from_this<T> (and the inheritance must be public as detailed at the link above; otherwise the mixin is useless)
3. Gets compiled with GCC with -Wnon-virtual-dtor (perhaps also with clang, I’m not sure)

you get warnings about the non-virtual destructor of std::enable_shared_from_this.

My question is – where is the fault here? That is…

• Should std::enable_shared_from_this have a virtual destructor? (I don’t think so)
• Should the non-virtual-destructor warning employ some criterion for when it is emitted (if at all enabled, that is)?
• Should the destructor of std::enable_shared_from_this be made protected? (And will this even work?)
• Should classes with this mixin not have virtual methods at all?

I’m confused.