In the UK children have a great diversity of ponies to ride. Shows are organised with age and height restrictions. It is rare to see a 14 year old riding a big horse let alone competing on one.
When I am in the US I see children on horses and it makes my heart miss a beat thinking how far they have to fall if they do.
Modern thinking seems to be that the bigger the better, not so! I am 5'8" and have ridden for a days Fox Hunting, 13.2 ponies and big horses. Over open galloping ground the big horse is the best but when it comes to hills and rough terrain, mountains and moorlands, give me the pony any day!
Majority of children grow up knowing that they will outgrow their ponies which will be sold so they can get the next size. It is just the norm.
I think I've mentioned this before related to this topic, but I'd usually prefer to see kids on horses than ponies. Why? If a horse is acting up then an adult rider won't think twice about hopping on to give the horse a lesson, or even ride the horse regularly in addition to the child. Many ponies are ill behaved because most of their riding is done by inexperienced children, and many people are hesitant to hop on to tune the pony up due to the image or being over weighted for the pony. As a result you get a lot of poorly behaved ponies. That's not true for every pony and many get by just fine without having adults on them, but it's true for quite a few!
Over the past few years I've seen a few fairly serious injuries (mostly broken bones) and nearly of these have come from ponies. A few from kids, and a few from quite experienced riders. I've seen an equal or greater number of falls from full sized horses, and I can only think of one that resulted in anything more than a couple of bruises. Perhaps it's just a coincidence, perhaps not. I haven't run the stats on it
When you're riding a horse that's small for you then your center of gravity seems to be shifted into an awkward position relative to the horse, so perhaps that explains the falls/injuries from experienced riders. I'm only 5'3" and I rode a 12.2hh pony at my old barn a few times. I used to ride ponies regularly, though all of them were in the 13 and up range, and I felt really awkward on this girl! Got used to her really quickly, but still felt like if she tried to duck out and I wasn't expecting it then I'd get tossed over her shoulder! Just because the fall is shorter doesn't mean that the risk of injury is necessarily lessened!
Either way, that's more of a side note than anything. The poster mentioned that she was looking in the 14.2hh range I believe and is an inch shorter than me, so I doubt that she'll be running into the pony problems!