Why does std::unique_ptr not permit type inference?

This is not an issue that's... unique to std::unique_ptr - instantiation of template classes does not automatically deduce the types from the constructors previous to C++17. This is why facilities such as std::make_unique, std::make_pair and std::make_tuple exist: they use template function argument deduction to reduce boilerplate.

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In C++17 you will be able to write:

auto foo2 = std::unique_ptr(new Foo());

thanks to class template deduction - assuming P0433R0 is accepted, which adds a deduction guide to std::unique_ptr.

The deduction guide is required because std::unique_ptr's constructor that takes a raw pointer uses the pointer type alias which is defined as follows:

std::remove_reference<Deleter>::type::pointer if that type exists, otherwise T*. Must satisfy NullablePointer.

Type aliases like pointer are non-deducible contexts, so P0433R0 proposes the addition of:

template<class T> unique_ptr(T*) 
    -> unique_ptr<T, default_delete<T>>;

template<class T, class V> unique_ptr(T*, V) 
    -> unique_ptr<T, default_delete<T, V>>;  

template<class U, class V> unique_ptr(U, V) 
    -> unique_ptr<typename pointer_traits<typename V::pointer>::element_type, V>;  

Which would enable class template deduction for std::unique_ptr.