This is not historically accurate. Insurance through employers came out of the federally mandated price controls during WW2, and was later solidified by massive tax breaks for corporations for providing said insurance (under the eager endorsement by unions among others). Changing the system would require changing the tax incentive. Changing the deduction to apply to individuals could be a path forward.
Federal mandates and tax incentives are created in the halls of legislation. This was mentioned above, albeit concisely. You even mention "massive tax breaks for corporations" which really only happens with intense pressure (backchannel or otherwise) on Congress. We call that "corporate lobbying" today, just as we called it back then.
Recall the intense pressures on FDR from both sides. Eventually the unions won some important concessions, but the corporations still had sufficient representation to ensure the system calcified into one that continues to funnel capital upward.
