So, you think the military is wrong by using .22lr as trainer? The groups don't open up that much, because it is the same trigger pull and the same sight picture. Look how many guys run a conversion bolt in their AR....same purpose, training. You get more trigger time for less money.
My son started shooting way before 9. He started on a Crickett single shot bolt action around 5. Shot that until he was 10. Then he moved onto the 15-22. You have no idea why my son chose the 15-22. Could it possibly be because dad has an AR-15? Because his uncle has an AR-15? And no, he doesn't spray 500 rounds an hour and have a grouping like birdshot. He consistently shoots a 5 shot group at 25 yards that a quarter can touch all 5 shots, from a rest, without optics. He earned his rifle merit badge in Boy Scouts on his first time out. My son also hunts and shoots close to 1 MOA with his .243 at 100 yards. But for just fun shooting, he likes the 15-22 with red dot sight.
Besides, the OP didn't ask if either of these were how we would start a kid shooting. He asked for a "fun shooting .22 for the boys", and for boys today, they would pick the 15-22.