"Medicaid for all" will mean more, not less, inequality when it comes to healthcare. Poor people will simply be at the end of a much longer line for services. Better educated, more affluent people will always have the means to get to the front of the line. They will now have free healthcare services that in the past they would have paid for. Many of them will consume these free services, thus making the line for healthcare longer.
What we need is true health insurance in a true healthcare market. Right now, there isn't a true market or true prices for healthcare. Insurance should be for catastophic circumstances, and people should pay for routine care out of pocket. If people bought policies based on real risk against illness, trauma, etc, insurance companies would be competing for business like they do with car, home, flood, etc. insurance. When you buy car insurance, they will pay you for damages to your car in a accident. They aren't paying for your oil changes, tune-ups, new tires, car washes, etc. They also don't tell you how to repair your car. They give you the value of your damages in cash. Then you decide how the repair will be made and by who. You control your $$$, and this leads to competition, quality, and innovation in the marketplace.
Right now health insurance companies try to enroll healthier people, and try to avoid higher risk people. This is because they have to charge the same for all. This is why many with pre-existing conditions have such a hard time getting covered. If they could charge less for lower risk people, and more for higher risk people, more people would be covered. And if they were competing against each other, they would be motivated to offer the lowest premiums they could.
Insurance companies now pay for many services that many people would pay on their own. People then consume services more often. This makes insurance and healthcare services more expensive for all.
When you are sick, you often have limited choices of who and where and how you will be treated. Limited competition equals less motivation to offer a better product at a better price.
Imagine what would happen if people paid for routine care on their own (you could still use HSA's and FSA's) and when something big happened your insurance company gave you the money to be treated. Then you decided who, what, where, and how you would be treated.
A true market for health insurance and healthcare services would equal better quality and lower healthcare costs for everyone.