"Burnout" though, may mean a gymnast isn't ready to move on. I "burned out", age 11, from high hours, high expectations, pressure, bullying coaches. Do I regret quitting? yes. But also I could not have carried on under that mental and physical strain. If someone had recognised that burnout, and re-adjusted my training, maybe said no competing for a year until you get back on track, I'd have continued in a heartbeat.
So I would describe burnout as not being able to continue, but not actually being done. We've seen many kids quit, only to return a year, two, sometimes 4 years later (check out Jessica Coombes, a UK elite athlete). If a kid is done and is ready to move on, no regrets, fine. But that's different to them just needing a different approach to continue…
In the sport DD is in now, elite kids do "quit". The coaches get together with the parents, and agree a schedule with the child so they can carry on in the sport. Switching coaches, competing lower levels, cutting hours, whatever it takes. If the child still wants to quit then so be it- but some just need 6 months with less pressure until they're ready to step up again, some want to stay in it for fun- but they do stay in it.
With regard to the "break" thing- I think it depends on the child. I could always take short breaks easily- in fact I came back feeling stronger and fully rested. If a coach is careful and builds in breaks to training, even if it's just two weeks at christmas and one other break, I think it can be beneficial.