Medical care is getting more and more expensive in many ways. This is why some people may want to buy into the Medicaid system. A doctor is likely to laugh at you if you happen to ask the question of can I buy into the Medicaid program? They will certainly wonder why you would possibly want to buy into the Medicaid program. Some doctors do not even accept Medicaid patients so I would personally much rather buy into a private insurance plan if possible. The people who need medical care the most are often enrolled in the Medicaid program.
If you called your Congressional representative and asked them if you could buy into the Medicaid program, they may consider it to be a fairly odd question. The Congressional representative would likely direct you to another state sponsored programs so you would be able to obtain medical care. Medicaid was not set up in the 1960's so people could buy into the program. It was meant for extremely poor and the children of the extremely poor who had no other way to get medical care. The disabled could also use Medicaid in order to get medical coverage.