I think it has a lot to do with a person's experience, though, as to the risks they are and are not willing to take. The few stallions I've had anything to do with, while generally quiet horses [even the Jazz son was nice with people, but with other horses he was a nightmare, extremely studdy and territorial], were not the sort of horses you would ever trust with a child. Even carefully supervised and with a capable, experienced person on the other end of a lead.
I didn't personally witness the following story, my mother did, but:
The stallion was a very quiet, very sweet gentlemanly Thoroughbred. He wasn't an easy colt to begin with, by all accounts, but somewhere down the line he was taught some very nice ground manners. He was easy to handle for everything, including breeding, and took his time to sweet-talk his mares.
One day he was brought into the breeding yard to cover a mare, but she had fallen for the teaser and didn't want a bar of him. He was put back in his yard and let loose, and he WENT his handler. Tooth and nail, out for blood. The stallion handler at this particular large-scale farm was a very athletic young man and this was bloody lucky as the fellow scaled the fence just in time to keep his life!
Why did this sweet, well-mannered stud snap? Who knows? Perhaps he saw the handler as a rival for the mare's affection. Perhaps he was frustrated because he'd gotten himself going only to be torn away from a mare that was heavily in season. [the men on the forum would know THAT feeling, all hot and ready and then told no!]
Either way, stories like that and the other one I shared are why I don't trust stallions. Ever. No matter how quiet or well-mannered.
My experience and that of experienced people I know has not been conducive to willingly trusting a stallion with a child!