You must be joking. Government never, ever saves money compared to what a profit-motivated private organization that has to compete with other organizations can do. For government all the incentives go the other way . . . hire more administrators, lawyers. Create subsidies for favored groups.
Streamlining? New York State lost money on off-track betting. How does a gambling operation lose money?
It’s fair to argue that single-payer will be fairer than the current system. But it’s foolish to think it will be more efficient.