TBH, I think it's generally the rider who gets bored of riding in the arena more than the horse. I know lots of people who almost never ride outside and their horses don't get arena sour. Just because you're always in the arena doesn't mean it has to be repetitive, either. There are tons of things to work on that can provide you and your horse with a change of pace.
At the same time, I have seen some of those horses, not even being able to be ridden form the barn, at a show facility, to the arena!
Yes, there are many things you can work at in an arena, as I have done many events, from rail classes, trail, reining, western riding , HUS, cattle penning, working cowhorse, games, but you still don't get a really broke horse, as those horses get their security form those walls, and not just from the rider.
Many also claim that their horse is just fine, stalled most of the time. Horses are, after all, creatures of habit
Bottom line, most horses are way better arena and show horses, if they are also ridden out