The last Harvard medical bankruptcy study, by David Himmelstein, had some holes in it. I haven't looked at the Woolhandler paper yet (the summary is free, but I'd have to request the full article, still behind the subscription wall), but she and Himmelstein have been single-payer activists for years, co-founding Physicians for a National Health Program.

Any science paper I posted here (on this or any other issue) that had this much political baggage attached to it would be immediately disregarded. Just saying.

But leaving that aside, if medical coverage were no longer part of the employment deal, employees would find changing jobs a lot easier. Keep in mind that unions are founded on the goal of near-permanent employment, and that a much larger pool of eager and qualified possible employees might not work in their favor as much as you think.