In the grand scheme of things, I don't think it made a huge difference to my life choices either (you can learn a lot about crappy jobs and bad bosses in a couple of weeks' "work experience")
Only adults think that any such thing as child-like innocence actually exists. Children see and hear everything.
As someone who's done his fair share of shit jobs before working in the relative comfort of the "tech industry", this was a valuable lesson in what is the reality of any work relationship (that is: "I work x hours and you give me x monies", that's really all there is to it...).
Lots of tech companies wouldnt get away with their "We're all a big family so you have to do unpaid overtime because we're all a family" bullshit if their employees went through dishwashing or other menial jobs before.
(Simplifying a lot for emphasis, but you get my drift)
Not that I regret my choices, but that 13 is just a little too young to be career-oriented, and 16 is probably the bare minimum. I was into computers at that age, but if my decisions were based on profitability or professional viability they would have been very different.
Don't underestimate the role of a crappy jobs and bad bosses, either. Hard to say you'd want anyone to experience that intentionally, but a wide perspective is priceless and can't be taught by explanation alone.