My concern with an AIO is what happens if the monitor dies? Having replaced my monitors once already during the life of my current machine (5 years old and waiting for at least one more year....please make it one more year), I am more worried about my monitors failing then my computer. Also, how easy is it to get in and blow out the AIO? I blow my case out at least once every 6 months, if not twice.
As for kids...I would get a mini box and build that...especially if they don't need a real powerful graphics card. Now, if they are going to be taking it to school (college or high school), get them a good 15 inch laptop (or 13 inch if it's not for gaming) By good, I mean cheap. It WILL get dropped, lost, sat on, dumped on the floor, etc during those 4 years. Either that, or get something that's designed to take abuse like a panasonic toughbook. That will be a lot more costly, but you need to figure out which will be the better value based on replacements/repairs over 4 years.
My company (non rugged) computer used to get repaired every year due to the large amount of traveling I did. Even though I was careful and always used a protective bag, it would still break on average 1x a year. That machine was always replaced before the warranty expired and given to some poor engineer that never left the office. Also, it wasn't just me...everyone in my department had the same issues if they were traveling with the frequency I was (I averaged something like 36 hours at home and 132 hours on the road each week for 4 years not counting vacation time)
Point is...college students put even more abuse on their laptops. If I had a choice, I would send any kids I had down with a desktop...a big honking one where the tower weighs 40 lbs so they are not tempted to move it. Then give them a couple of pens and a notebook (and MAYBE a tablet or smartphone) and say..here..learn to take notes the old fashioned way.