What is important to remember about Medicaid and similar programs is that you can sign up when you need care. People with private insurance can only sign up during open-enrollment periods.
Sure, the people who sign up for Medicaid will consume a lot of medical care and then drop off. But they will also drop out of Medicaid until they need it again. Meanwhile, eligible people who become sick will sign up next month. It never stops.
And it certainly does not address the problem that Medicaid provides poor access to physicians. If it did, the newly covered would not have had to flood hospitals’ emergency departments.