Well, let me play devil's advocate.

Really, there's no need. It's already been definitively proven to be harmful both to children and society.

You don't need a two-way binding contract to form a labor relationship. You could have a relationship where an employer offers a child some terms, and the child can work whenever they want, leave whenever they want, and get paid for the time they work, or for their output, or something.

No, you really do. The power differential is far too great to be able to rely on "they can leave whenever they want". Adults have significant physical, social, cognitive, financial, and legal ability that can be easily exercised to coerce those who are still developing, even unintentionally.

Does the labor cause the poverty, abuse, and crime? I'd imagine that the poverty causes the labor, and the poverty also causes the crime.

Yes, it is casually connected. Child labor causes time that would spent learning to instead be spent related to labor and recovering from labor. This in turn causes reduced academic performance, increasing the likelihood of poverty, which in turn causes increase in criminal behavior.

Abuse might also cause the labor, as parents could force their kids to work, but you could create systems at certified child employers to interview Children and see how their home lives are going. The children might also be using work as an escape—either a temporary one, or a way to save up money to move out as soon as possible.

That is the role for not-for-profit enterprises dedicated to child welfare, not those looking to exploit children for personal gain. Abuse is also endemic in most areas of current and historical child labor.

Generally, when people talk about the age of meaningful consent, there's a clear line at or near the age of majority. Where's the line where you can meaningfully consent to labor? Does it depend on the job? Sure, five year olds shouldn't be allowed to work at all, but what about a fourteen year old who really wants to be a camp counselor during the summer? I worked at a park when I was 16, I mostly sat around all day. I read three books (the ones I had to read for school and one more), I went for a walk every day, I got fresh air, I talked to people. Surely we can agree that that was fine.

Participating in education with a nonprofit organization with increased oversight and not having profit motive to exploit children when also outside of the usual academic year? Yup. That seems reasonable and a good way to allow them to learn responsibility and contribution to society in a safe environment.

We should definitely talk about the types of job. No kid should be a factory worker or an accountant or a dentist. But working in a park, being a camp counselor, babysitting... There are many traditional jobs that apply to children with no risk of physical injury, jobs that don't conflict with schoolwork, etc. Do those studies address each form of labor?

Many of the "jobs" that children can participate in without harm are better lines at through the lens of education. They have to be strictly examined to ensure that they are not setup for exploitation and allowing any for-profit activity significantly increases this risk. Arguably, some traditional jobs such as childcare should only be acceptable if matching the going rate for adult childcare workers as, while useful in learning child-rearing skills that may be needed as an adult, it is used to suppress wages of those who do so vocationally.