They should add some light premiums, deductibles, and copays to lower costs and steer behavior.
That wouldn't be single payer.
Many healthcare systems that are considered single-payer, including Medicare, include modest premiums or other out-of-pocket expenses.
Technically, deductibles and copays would make it not
single-payer, but in that case, there would be no such thing as a truly single-payer healthcare system. That's like saying people with insurance that include deductibles and copays are partially uninsured. As long as they are measures for financial viability rather than barriers to participation, you can call it universal, public, and single-payer healthcare.