Which plan would we be talking about for government coverage? I assume barebones plans.
In that case, it still matters who you work for, because some employers still provide much better coverage.
About 1.28% of US gross domestic product is spent subsidizing employer health plans: https://www.cbo.gov/system/files/2022-06/57962-health-insura...
But just want to point out that "low end" Medicaid plans are frequently better in many ways in states where the program is well supported as far as coverage vs middle-of-the-road employer plans. Zero out-of-pocket expenses, and in Oregon, Washington and California they cover routine dental care as well, for example.
They typically have very restricted networks however vs employer provided plans.
Instead of your employer paying you $S salary per year + paying $M per year for the premiums for whatever group plan they use they would pay you $S + $M salary and you would buy whatever health insurance you wanted directly.