Looping with variables is very easy to execute by hand.  Recursion
with parameters is harder to execute by hand, especially when the
human is not told about tail-call shortcuts.  Most programming courses
spend all their time on how to execute if-then-else, how to execute a
while loop, and how to execute recursive calls.  Therefore looping must
look simpler than recursion.

Recursion is more handy in solving problems.  To add up 10 numbers,
you just have to know how to add up 9 numbers and how to account for
the 10th.  To find a number in a sorted array of size 16, you just
have to know how to find a number in a sorted array of size 8 and how
to decide which 8.  Solving a problem by divide-and-conquer or
reduction is a natural instinct, and we do that all the time, inside
or outside programming.  In contrast, to solve a problem by looping,
the approach is either trial-and-error (which ironically is itself a
loop:

0:  clue := empty
1:  P := "while ? do ?"
2:  repeat
3:    P := genetic mutation of P using clue
4:    r := result of executing P 1 time, 2 times, "many" times
5:    d := difference between r and expectation/specification
6:    (* as a result there is always a bug when P is executed 0 times *)
7:    clue := clue U some conjectures made from d
8:  until d is empty
9:  return P

) which is tedious, error-prone, and seldom convergent; or refinement
rules based on loop invariants, which is Greek to most people.
Writing a working loop is swim-or-sink in education and dark magic in
practice.