Nobody specifically wants to outlaw that. Literally nobody. Laws have to have a tradeoff between being too general and being too specific (and having too many special cases). Being too general means catching too many edge cases where it does more harm than good. Handling too many special cases creates a moral hazard where there's more benefit in finding loopholes or plainly ignoring poorly enforced parts of the laws than honest work.

Anecdotally, I did work as a kid, didn't learn anything useful, did not learn responsibility, a bit of money I didn't really need, and it felt like a waste of time and left a bad taste overall.

I fully believe that in many, possibly most cases, work is beneficial for kids (as long as they're not from poor families in which case there will be too much pressure to overwork, affecting school/homework and taking away whatever little time they have to enjoy childhood).

I addressed this in other comments, I only want that a normal (full time) job pays for a living, I did not want to discuss all kind of edge cases and so it may not apply to your example. But if working at an ice cream shop is sufficiently easy to learn within a few days and the kid does all the same work including cleaning up and what not, how would you justify paying less than to a regular employee doing the same work and having to live on that income?