We have a medical/insurance system that breaks people up into tiers.
At the top tier, you have people with Cadillac insurance, with modest premiums deducted from paychecks, low deductibles and co-pays, and high caps on benefits being provided, often by companies that don't do a lot of squeezing on healthcare providers (relatively).
The next tier consists of people with lower-quality insurance, they have higher deductibles and co-pays, and not as much of their needs (psychiatric, for instance) are covered. That's where probably most people are.
The next tier after that is the folks on Medicare or Medicaid, or some other such governmental system. They have to be able to find healthcare providers that will take the lower reimbursement payments offered, and those providers know they're not going to recover all of the co-pays, deductibles, etc., so they build that into the acceptance rate of those patients.
At the bottom are people with zero insurance, who get charged the full rip-off price for anything, because they're not "members" of some sacred group, and they often face the choice of doing without necessities to pay a bill, or filing for bankruptcy. They pretty much get emergency care only, and don't often bother to seek timely treatment from the healthcare industry.
When unions negotiate top-quality benefits for their members and the members' families, the employers see the value of putting these workers into that top tier. The employees have less financial stress, and can get in sooner to better quality providers, and be back on the job sooner.
Medicare-for-All lumps all of us into one tier, and that's threatening to people in the top two tiers.