Some of the gap may be illegal/undocumented children.
Some of it is families in the gap where they can't get employment that pays fully for family healthcare, but make too much to qualify for CHIP/Medicaid.
Some will have been disqualified for other reasons, perhaps.
> Some of the gap may be illegal/undocumented children
Do we know what fraction? If most American children have access to healthcare–a claim I'm sceptical of–then I'm not seeing an urgent problem that has to be solved by the healthcare system.
To be precise "have no health insurance" and "have access to healthcare" are not two sides of the same coin.
Everyone in the USA has access to emergency care and stabilization, the practical results of which are that for emergencies, you get helped, payment is worked out later.
If you have no problem with having no intention of paying, the system absorbs the cost.
If a child isn't covered by medicaid for income reasons, then CHIP is a program that kicks in to cover kids at higher income levels. These are all federally backed state run programs though so it's going to be hard to figure out exact details and surely someone is slipping through some cracks. Some states combine the programs, some have both. They can vary on the income levels. There is also some level of transition as the paperwork can be cumbersome, unclear and confusing, so kids may be kicked out of the programs while these processes play out, usually with retroactive statuses of eligibility.
Some of it is families in the gap where they can't get employment that pays fully for family healthcare, but make too much to qualify for CHIP/Medicaid.
Some will have been disqualified for other reasons, perhaps.