I've seen both sides of the coin. I think that a mini in the hands of a kid who has GOOD, EXPERIENCED horse people on call 24/7 is absolutely not an issue. However, they ARE ponies, and they ARE very smart, so can't be allowed to get away with anything.
When I was 9, Mum bought a 3yo shetland/mini cross colt, with the intention that he would be gelded, and that we would break him to saddle, and he would be my birthday present. He was a bitey little monster but he WAS a colt, so that was hardly unexpected. It probably would have improved had we had him long enough to get him gelded. Unfortunately we weren't allowed to keep him in our backyard and the fences where Mum kept her QH were not going to be sufficient to keep a mini in (not to mention the paddock was WAY too big), so we had to sell him. It was probably for the best, looking back, because I was a pretty capable kid but definitely not experienced enough for an unbroke stallion.
Now, nearly 8 years later, I have my first foal. She is also my first unbroke horse that I have the intention of starting myself. I have had a freshly broke horse before, but he doesn't really count because someone else did all the work. And I, being 14 and sure I knew everything, undid it all and had to fix my own mistakes.
IMO kids are fine with a well broke mini that knows its manners. I know a few people who actually have mini's because their kids' confidence is so low that they can't handle big horses, and with the RIGHT mini, that arrangement works brilliantly.