I will say that when I have been in the US my heart misses a beat when I see small children on horses rather than small ponies. If they do fall then the damage is surely going to be greater?
LOL, it's amazing how growing up in a different culture can create such different views. I have always wondered why more people don't have their kids on full sized horses rather than ponies.
The way I see it, if a child's horse needs a tune-up, then it's big enough for just about any adult to climb on and do the tune-up. However, if they are riding a <12 hand pony, then not just anyone can train it or tune it up...and I believe that's why I see so many ill-mannered and ill-trained ponies. Most decent horse trainers I know are good sized men who couldn't ride something so small without hurting it.
But, I grew up in a ranching lifestyle where a kid's first horse is generally their dad's old ranch horse who has been a zillion miles and seen/done just about everything a horse can see/do. That's what I always rode growing up, the horses that my Dad owned and trained to be show/roping/ranch horses, then my older brother would inherit them, then I got them after he moved up to a different horse.
My first "horse" was a mini burro that gave me my first taste of getting bucked off because the only person who was small enough to "train" him was my older brother...who was all of about 7 at the time.
However, this was my first real
horse and I never took a fall or got so much as a bruise in all the years I rode him.