Sure they do. My first few jobs were paid under the table for less than minimum wage in the late 90's. Those businesses are still around and still employing youngsters at that age. They keep it quiet because it's illegal; you have to know someone.
At those first jobs, I received secretarial and retail training and experience. This didn't help me at all when I applied to actual paid positions at retail stores. Nobody gave a damn about my retail experience when I was interviewing because they see it as "unskilled labor". They can hire anybody off the street and teach them to use a register. It also didn't matter when transitioning to programming since they didn't care about anything other than if I could program.
I struggled just as much as your kids did at getting started in the workforce. There's a huge gap between skilled and unskilled labor. The unskilled labor positions are also few and far between. There are too many applicants and not enough positions. For skilled labor, there's a huge gap between what you're taught in college and what's valuable to an employer, but that's another conversation.
The average 35, yr old min wage employee isn't impressed that her wage is governed by a law intended to apply to a mythical teen that could be doing her job.
That's great, if the job has enough economic benefit to the employer to cover minimum wage. Once upon a time, it was common for early teens to get their feet wet in the job market by e.g. sweeping a gas station parking lot or washing windows. These were activities that provided some marginal value to the employer, but not enough to cover the current minimum wage. Those jobs don't exist any more.
Instead, kids have to convince an employer that they can provide a much larger return, but with no work history. They also have no way to gradually "ramp up" into the work force. My older kids struggled to get started in the workforce as a result.