Isn't the thinking that these jobs are supposed to be for teenagers, which has their income supplemented by their parents?

For a babysitter, that seems fair. For most minimum wage jobs, though, no. They are not just filled by teenagers until they can get a "real job." If you look at charts 1 & 7, you'll see most people working at or below minimum wage are 25+.

https://www.bls.gov/opub/reports/minimum-wage/2017/home.htm

Why should a working persons age or living arrangement cause a devaluation of the work they are doing?

Yes the instinct is to pay teenagers less because we generally cannot fathom them capable or experienced enough to do “real” work. But does this set the stage for the devaluation of entire classes of work because they’re seen as “for teens?”

They are not. But some low paid jobs exist only because they are interesting to certain demographics and some people are willing to pay for it; think about the paper boys or lawn mowing adolescents - it is the kind of thing I can do myself (I find it relaxing), but I pay for it only because it gives someone else the opportunity to have some extra pocket money easily. It is a good arrangement with your kids or some neighborhood kids and in rural areas in my country (Europe) it is sometimes an arrangement also for a nanny. In many cases the money I pay is more than the value I receive, but I still choose to pay. If someone feels the need to pay $40 for 3 hours for a nanny that is fine, but that does not make it automatically worth $40.

> Why should a working persons age or living arrangement cause a devaluation of the work they are doing?

No, but their living arrangement does affect whether it's possible to live on that wage, which is what GP was talking about.

Is the job worth less if done by a teenager?

I know some people that do low paid work as an extra, not to live on it. $280/week is over 10 times my salary at my first full time job and I was supposed to live on it. It's all relative, without enough context it is meaningless.