Why can't the C# constructor infer type?

Why is type inference not supported for constructors the way it is for generic methods?

public class MyType<T>
{
   private readonly T field;
   public MyType(T value) { field = value; }
}

var obj = new MyType(42); // why can't type inference work out that I want a MyType<int>?

Though you could get around this with a factory class,

public class MyTypeFactory
{
   public static MyType<T> Create<T>(T value)
   {
      return new MyType<T>(value);
   }
}
var myObj = MyTypeFactory.Create(42);

Is there a practical or philosophical reason why the constructor can't support type inference?