This issue (like most things when riding a tandem!) comes down to the skills of both riders, their ability to communicate, and whether they cooperate & coordinate on the bike. Some teams achieve perfect in-sync flow, while others can barely get on & off the bike without chaos.
While it may be true of some teams that, "stokers have one job, pedal. This can be boring for them," it is far from true for my wife and me. While it's accurate that steering, braking, and shifting are controlled by the pilot, there's a lot more that goes into riding a tandem (or a single bike for that matter!) For example, we've learned over the years that the stoker actually has a HUGE amount of control over cornering and flow, whether riding on pavement or dirt. The more focused and active she is, the faster and more smoothly we ride. She's also the chief radar operator, alerting me to potential traffic threats, other overtaking riders, etc. On long straight sections, there's not really much for either of us to do (although a good pilot is always vigilant), so we chat about sights along the road, life, whatever--which is one of the great joys of tandeming for us. I don't think that either one of us has ever been bored while riding.
All of that said, teams are very different. I completely understand why a pilot with a less-experienced stoker might not want them braking. Likewise, I can see why a more experienced stoker might not trust an inexperienced pilot to shred a steep & technical descent. I very much believe that every team needs to find their own groove, while always embracing opportunities to learn, adapt, and improve.