Medicaid is a very mixed bag - and varies a lot by state. My experience, with about 35% of my patients being on Medicaid, is it does a good job of giving patients access to unnecessary stuff (free Tylenol!) and major stuff (hospitalizations, major surgeries, etc), but it drops off a lot of services in the middle, and it adds a lot of work to providers and dumps a lot of costs off on others.
I get paid the same regardless of what insurance my patients have, but I have have to do way more fighting with our Medicaid plans than with any other insurer to get patients what they need.
Medicaid is oriented toward people with low income so there are no co-pays - whatever gets covered is fully covered, and there are things like taxis to appointments and OTC meds like Tylenol, and infant vitamin D drops that Medicaid will cover, but private insurance won't. They try to minimize these costs by making you fill out tons of paperwork though.
On the other hand, there are many things that are much harder to get covered. The WA State Medicaid plans (Molina) have very restrictive and often arbitrary formularies for prescription medications. For example, they cover the mildest topical medication for acne, but if that's not strong enough, the doc has to jump through hoops to get stronger medication, even though it doesn't cost any more. And here, no durable medical equipment is covered, meaning if a doc gives a sling, walking boot, or crutches, Medicaid won't pay for it. In practice, the provider's office ends up giving the equipment away because they can almost never collect from the patient either. Medicaid dumps the cost on the doctor's office.
Also Medicaid is exempt from many of the ACA requirements for covered services. So while the ACA mandates that plans cover certain preventive developmental screenings, our Medicaid plan doesn't pay for them. What a nightmare trying to figure out how to bill certain (non-grandfathered) private plans, but not Medicaid or grandfathered plans. It is pretty much impossible, so we just don't bill for these services, and eat the costs.
Average Medicaid reimbursement is about 60% that of private insurance, so many providers won't accept it. There was a time in the greater Seattle area that no orthopedists accepted Medicaid other than Univ of Washington and Seattle Children's. It was an access nightmare. That said, I only have so much sympathy for guys making as much as the orthopedists make...
Where we are, mental health contracting with Medicaid is also a mess. They have the state divided into regions, so someone with the exact same Medicaid plan in county A where wait times are months, can't see a psychiatrist in county B where wait times are a few days, even though both psychiatrists accept the exact same Medicad plan.
Dental can also be variable. In many cases they will pay for extraction, but not implants. So you can get dental care, for free, but that means a hole in your smile where they pull a tooth, but nothing to fill that hole. Many dentists here accept Medicaid when they first open their practices, but once they start filling up they don't take Medicaid any longer because it reimburses much lower.
Anyway. Despite all of the above, I would gladly take a single payer system in the U.S. If everyone had Medicaid, things would even out, and Medicaid reimbursement would have to go up since there wouldn't be anyone else to eat those costs. The variability is a nightmare, so having one uniform plan, at least we would know what is covered consistently, and not have to deal with so many different players who all follow different rules.