They absolutely can enact universal healthcare, and some have tried in the past. Vermont famously(?) did this with Green Mountain Care - the problem is that when it comes to healthcare you end up needing to pay the same outrageous market prices for healthcare that insurance drives but without any of the wink and nod discounts that HCPs and Payers exchange to keep things moving - along with a lot of market players working actively to extort as much money as possible from your system.

Universal healthcare is difficult due to the inability to actually nationalize health care providers without having your state's system overburdened by everyone from neighboring states which you're quite limited in restricting due to federal interstate commerce requirements. Also the federal government would probably come down hard on you.

Some have at least moved incrementally in that direction by referendum. Maine, Missouri, and Oklahoma voters opted in by ballot initiative to ACA's Medicaid expansion, after their respective state governments had decided not to expand Medicaid. That's admittedly easier than designing an entirely state-level system.