“Double longing and flexions are much better to create throughness.” True. And that has absolutely ZERO to do with the OP, which is little kids (and beginners) riding with side reins to give the poor horses a break, but mostly to teach them what it feels like so they can learn to duplicate that feeling. Beginners aren’t “creating throughness” because they are a long way from understanding what that means, let alone feeling how to accomplish it.
Introducing riding with side reins does not create a crutch for the ride as do draw reins.
I was introduced to the riding-with-side-reins-on-a-school-horse concept by a German Trainer long ago. I think it’s fine. I don’t teach up/down lessons as a rule, and I don’t use side reins routinely, but I certainly will slap them on there once in a while if I think the rider’s hands are rough or they have trouble with contact.