"This task can also be solved using iterative solution, but it’s way more complicated because we would have to nest for loops but don’t know how deep they are nested. The unknown number of nested loops is a common characteristic of all problems that are recursive in their nature and should give you a hint that recursive solution is required."

Would suggest instead something like

"We could solve this directly by managing our own stack of work done and keeping track of where we are in the problems as we divide them up, but it's easier to take advantage of the fact that the programming language is already providing us a call stack that can do this work for us."

Then, later, you can point out that this also helps with the backtracking solution as the programming language is maintaining the old environments; if you were iteratively managing your own stack you'd also have to backtrack manually.

Because that's how you transform a recursive call into an iterative one, not nested for loops. The general points made in the article still hold up, of course.