Properly adjusted side reins help a horse maintain balance in forward movement and transitions and are especially useful to young horses who do not yet have the musculature to maintain the bridge from stride to stride. They teach the horse that going forward into a soft yet steady contact with the bit is “okay” and they can trust the bit and rely on that contact. That kind of introduction to the bit is actually a kinder way to start youngsters than having their mouth hit by a rider trying to stay in sync with a horse who has not yet learned how to keep itself in balance in movement - and again, esp. when it does not yet have the musculature to hold itself in balance. And don’t forget that a young or green horse just learning to stay in balance while moving back to front has a much harder time doing it carrying a rider than in carrying just itself - even when the rider is gifted in keeping his/her own body in control.
Posting a photo of incorrect and abusive use of side reins or draw reins with the insinuation that all “experts” use that technique is hyperbole intended to inflame the passions of the uninitiated. As in all things in the equine world, there are “experts” who cross the line and abuse their power over the horse via improper use of “gadgets” and techniques, and “experts” who properly know when and how to use a gadget or technique and who train using a kinder, gentler, and more emphatic approach.
I will also add that except on rare occasions or in institutions such as SRS or Cadre Noir, the proper use of side reins - even proper lunging techniques - is sadly not taught to people who are starting out on their journey learning how to train. People may get a 60 second lesson one time on how to use side reins, which they promptly forget - or don’t really grasp - and there is no “master trainer” who checks their equipment every single time they lunge or ride and watches their sessions with an experienced and keen eye and is ready to jump in and correct things as needed. The old art and the old masters are fading away, to be replaced by the likes of Helgstrand, Parra, van Baalen, van Grunsven, Janssen, Kittel, etc. - and it is a travesty that they will one day be considered the ODGs of dressage.