Medicare for all, is sound policy that will lower cost for the average person. Premiums, deductibles, copays and all private taxes or so called fees, would be completely gone and be replaced with a lower total replacement fee to government, a substantial part being paid for by people with an immense amount of wealth. Thus most americans would pay substantially less for their medical care. So yeah, not costing people "extra", rater less.
Also, Obamacare or Romneycare was a vast improvement to many peoples healthcare, but it was severely lacking on many fronts, for one it did not provide a public option.