It’s useful to separate medicine from ER in healthcare discussions. In ER, there is no market. In healthcare, we have a deeply-flawed market. But in most zip codes, there is some competition.
It's being reduced though. A lot of private practices are being bought out by big (in many cases for-profit) hospital or doctor's groups, and the doctors are put on salaries instead of owning their practices. In many areas there is now only one big group. Naturally this can be highly profitable.
In part due to access-to-care issues. More competition in medicine should increase access thereby reducing ED use. One that comes to mind are in-house visits, something expensive for no good reason in America.