Try to avoid adding additional agencies and systems together. It creates red tape, and increased admin costs, which means people waiting to get care, and having avoidable complications while the issue of who pays the bill gets settled.
Fed level medicaid, coupled with state level healthcare is such a beast.
Rather, I would much prefer to see the Fed issue minimum care universal mandates, with each state possibly providing better care than that.
EG, Fed says "You will provide, at the least, this level of healthcare" which covers routine dental, routine cancer screening, routine surgery, etc. You can be assured that anywhere in the US, you will get that level of care. The state itself still foots the bill. It will eat a little when people from out of state get injured and treated in-state, but a properly balanced healthcare system can absorb that, by planning for it.
In addition to this minimum level of care, individual states might offer better service than the fed required minimum. Say, they might also cover psychiatric and psychotherapy services, in addition to mental health medication providence, or whatever. Maybe you can get state funded sex changes. Whatever. Things that are outside of the minimum requirement, but make the state a better place to live in, (and thus encourage migration to the state, bringing useful skills and other resources with them, and increasing the wealth and prosperity of the state.)
That means that if you went to California, you might get better healthcare than if you wen to Arkansas, but regardless of which state you were in, you would still get dental, life saving surgery, etc-- subsidized by the state govt, who gets it provided at cost.