I can think of a few arguments against billing insurance and Medicaid.
1) By taking insurance money, particularly government (Medicaid) funds, they are opening themselves up to investigations and charges of fraud. I’m sure some will respond that they should simply follow all regulations and there won’t be a problem, but some of the regulations can be confusing and unintentionally violated, plus, a motivated prosecutor can cause trouble even when everything is legitimate. There are several such cases, some more famous than others.
2) We don’t want insurance companies or the government having any say in how care is provided.
3) You have to bill everyone. Aside from the legal issues of only collecting from insurance but not from individuals, people will hesitate to call Hatzala if they know they’ll be getting billed. Theoretically, it shouldn’t make a difference, but practically it will.