You should talk to some people with kids then. I can't find the source, but I think the US national average is something like $1500/month for <40 hour/wk daycare. That doesn't account for child-to-sitter ratio differences, or cost of living differences either. A few different friends around the country, not in big cities, have cited >$5K/month as the cheapest they can find for full time daycare. It's significant enough that families with multiple children are often cited as being unable to have both parents with careers, because the cost of childcare far exceeds what one of them can make in their career. To be fair, this makes some sense, you're effectively paying for a portion of a child care professionals career, plus the shared overhead for facilities and supplies. If you have a decent (<8 children per professional) ratio and have 2-3 kids needing daycare, you're paying for 25-30% of someone's direct salary, plus overhead. Very few people make so much more than a trained professional that they could afford to shell out that much.

It's actually cheaper now. the numbers I quote were from when my children were in barnehage many years ago. But remember that is the maximum one would pay, it's graduated according to your income. The rule now is not more than 6% of household income and not more than about 130 USD per month. Also remember that this is eight or more hours per day five days a week in a facility that doesn't only look after your children but also teaches them how to be independent, resilient, social, etc.

Could you get private child care for 300 USD per month?

Pre-school nurseries in my area typically charge around £100 ($132) per day.

i just got quoted 300/wk for 2-day daycare

What do you mean?