Sure we could ban child labor, but then millions of children would be out of a job.
I'm only half joking – the problem with this argument is that it can be used to justify almost any injustice or inefficiency if there is a cost to fixing it.
You are right to flag the issue, and most serious proposals to introduce single payer healthcare in the United States also lay out a transition plan for health care workers to move from the private to public sector.