Proposed resolution:

This wording is relative to N4606.

1. Modify [any.cons] as indicated:

   template<class ValueType>
     any(ValueType&& value);
   

   […]

   -7- Requires: T shall satisfy the CopyConstructible requirements. If is_copy_constructible_v<T> is false, the program is ill-formed.

   -8- Effects: Constructs an object of type any that contains an object of type T direct-initialized with std::forward<ValueType>(value).

   -9- Remarks: This constructor shall not participate in overload resolution if decay_t<ValueType> is the same type as any or if ValueType is a specialization of in_place_type_t.

   […]

   template <class T, class... Args>
     explicit any(in_place_type_t<T>, Args&&... args);
   

   -11- Requires: is_constructible_v<T, Args...> is true.

   -?- Remarks: This constructor shall not participate in overload resolution unless is_constructible_v<T, Args...> is true

   […]

   template <class T, class U, class... Args>
     explicit any(in_place_type_t<T>, initializer_list<U> il, Args&&... args);
   

   -15- Requires: is_constructible_v<T, initializer_list<U>&, Args...> is true.

   […]

   -19- Remarks: The functionThis constructor shall not participate in overload resolution unless is_constructible_v<T, initializer_list<U>&, Args...> is true.

[ 2016-07 Chicago ]

Monday: P0 - tentatively ready

The in_place constructor that takes an initializer_list has both a Requires: for is_constructible and a Remarks: for is_constructible. The one that takes just a pack has just a Requires: for is_constructible.

I think both of those should be Remarks:, i.e. SFINAEable constraints. Otherwise querying is_constructible for an any with in_place_t will not give a reasonable answer, and I utterly fail to see any implementation burden in SFINAEing those constructors.