So is it arguably better for everyone or should there be protections for the children (who are presumably part of "everyone")?
I think if you immediately include a disclaimer about the children you probably don't believe there is much of an argument to be made.
If I look at it strictly in terms of child labor, there's nothing stopping those opposed to child labor from leaving Virginia and/or discriminating against products made there. Just as we can today with products produced by brands that we know use child labor.
My point is, in the hypothetical situation that a state did allow child labor – which I do not at all condone – people could choose not to buy products from that state, as people already do in not buying products from certain brands and countries that use child labor.
A US state can't do this on it's own because they can't force everyone to participate and they can't reject entrants from outside. In the Virginia/Maryland example Maryland would face an exodus of healthy and productive people who want lower taxes and an influx of sick people who want the free health care. It's not about "remaining equal in all other categories." It's that it wouldn't really work at all.
That's why you can't really have a system with massively different social services at the state level: the unbridled state to state migration.
On "unbridled state to state migration", I already covered that. Maryland would have to face the real cost of providing universal healthcare, and residents would have to decide whether it's still worth it to live there. Many sick people would decide that it's not, and choose to stay put in Virginia.
And if it truly wouldn't work, then it begs the question: Does it really work on the federal level? Why are costs skyrocketing and providers leaving exchanges?
The point is that they would have to face much more than the real costs of providing universal health care because they would have to provide care to a lot of people that never paid into the system due to migration.
In your example of child labor, it's arguably better for everyone if Virginia can produce cheaper goods. (Please don't think I'm in any way arguing for child labor.) Maryland benefits from the cheaper goods as well, and is able to free resources for other pursuits that are economically advantageous for them. We already see this to a degree in places that have an abundance of a natural resource – it's cheaper and more efficient for them to export the resource than it is for other places that don't have the resource.