Iterators of any kind are just a form of recursion, i.e., a thing "using itself". For example, the basic equation governing the while loop is
(while b do C) =
(if b then (C; while b do C))
You may think I am doing something exotic, but as soon as you try to explain what recursion and iteration mean, you will end up writing such equations. For example, people tend to explain the
while loop by saying things like "and so on" (imprecise) or "do
b" (not explaining anything), or "keep doing" (circular explanation). The above equation tells you everything there is to know about the
while loop. Similar arguments can be made about other forms of iteration.
The above equation is recursive, as the defined term appears on both sides. The general form is $$x = \phi(x),$$ which of course is just a general recursive definition of $x$. In this sense iteration is just a special form of recursion. So as far as theory is concerned, there is pratically no difference between recursion and iteration, except that the latter is a special case of the former. And both concepts are special cases of fixed point equations, a very important and general mathematical concept. This answers why "they chose recursor instead of iterator".
Your claim that iteration is more efficient than recursion is bogus. Modern programming languages are quite efficient at both of these tasks. In any case, it is not the job of humans to think about low-level details of execution of programs (maybe that was the case in the 1960's when the total amount of CPU power and memory on the planet was comparable to what kids carry in their pockets these days). We have better things to do as programmers, such as how to write programs most efficiently and how to make sure they are actually correct.