I strongly think that covering everyone in the existing system is not the best way to go.
The existing system is designed to cost as much as possible, and we have way too much demand for treatment (as is) and not enough supply. ER wait-times aren't 2-4 hours just because.
First, that needs to break.
Then, you can cover everyone.
We simply do not have enough doctors for how many old and unhealthy people we have. We should be thinking about how to keep people from going to the hospital that don't really need to be there. Do you really need to go to the ER because you stubbed your toe? If you didn't have insurance, you'd go to a low-cost clinic and get the same treatment for 1/10th the price.
We are slowly getting there already. Low cost clinics weren't widely available, but they are becoming more and more available as the cost of health care even WITH insurance is too high for most people.
The infrastructure for the bottom ~50% of people needs to exist to break free from a system that is not designed for them BEFORE they can move off it.
It's almost there.
Since One Medical became widely available, I basically have not gone to the hospital in 5+ years. Before, you kind of needed to go even for routine things (or at least I didn't know of a viable alternative). More and more places like this are springing up all over the US.