Why is allocator::rebind necessary when we have template template parameters?

Question

Every allocator class must have an interface similar to the following:

template<class T>
class allocator
{
    ...
    template<class Other>
    struct rebind { typedef allocator<Other> other; };
};

And classes that use allocators do something redundant like this:

template<class T, class Alloc = std::allocator<T> >
class vector { ... };

But why is this necessary?

In other words, couldn't they have just said:

template<class T>
class allocator { ... };

template<class T, template<class> class Alloc = std::allocator>
class vector { ... };

which is both more elegant, less redundant, and (in some similar situations) potentially safer?
Why did they go the rebind route, which also causes more redundancy (i.e. you have to say T twice)?

(Similar question goes to char_traits and the rest... although they don't all have rebind, they could still benefit from template template parameters.)

---

Edit:

But this won't work if you need more than 1 template parameter!

Actually, it works very well!

template<unsigned int PoolSize>
struct pool
{
    template<class T>
    struct allocator
    {
        T pool[PoolSize];

        ...
    };
};

Now if vector was only defined this way:

template<class T, template<class> class Alloc>
class vector { ... };

Then you could just say:

typedef vector<int, pool<1>::allocator> int_vector;

And it would work perfectly well, without needing you to (redundantly) say int twice.

And a rebind operation inside vector would just become Alloc<Other> instead of Alloc::template rebind<Other>::other.

Answer 1

A quoted text from Foundations of Algorithms in C++11, Volume 1, chap 4, p. 35 :

template <typename T> 
struct allocator 
{  
   template <typename U>  
   using  rebind = allocator<U>; 
}; 

sample usage :

allocator<int>::rebind<char> x;

---

In The C++ Programming Language, 4th edition, section 34.4.1, p. 998, commenting the 'classical' rebind member in default allocator class :

template<typename U>
     struct rebind { using other = allocator<U>;};

Bjarne Stroustrup writes this:

The curious rebind template is an archaic alias. It should have been:

template<typename U>
using other = allocator<U>;

However, allocator was defined before such aliases were supported by C++.