Because of the premiums they have to pay, you mean? The premiums are currently about $150 a month, or less if you accept a higher out-of-pocket payment. If you don’t earn much, it’s almost 100% subsidized by the government, which is mostly paid for by people with higher incomes who pay more taxes (in absolute numbers as well as relatively, due to the progressive tax system).
I think one of the most important factors for not having children early is the sky-high housing market, definitely not the healthcare insurance system.