Defining class by income seems odd. It’s also household income, which feels off if there’s potential to be hiding large childcare costs for dual income houses. Disposable income seems like the better metric ideally to me.
A dual income household where one person’s income is going almost entirely to childcare is effectively a single income household and NOT in the same class as a dual income household without that cost pressure. I don’t see how that difference could be seen as artificial.
Parents want their children to be safe, healthy, happy and nurtured. They will pay for services to provide that, and whether we label that service daycare, babysitting, school, summer camp, nannying, extracurriculars, etc doesn't seem like it makes much difference.
Childcare is a legal necessity. Private school education is not.