There are all kinds of savings in a single payer system. You eliminate the overhead of dealing with disparate billing systems. You can more easily find waste

There are all kinds of savings in a single payer system. You eliminate the overhead of dealing with disparate billing systems. You can more easily find waste and fraud since all data is flowing into one place in a single comparable format. And, most importantly, you have the power of being the only buyer in a market which can pretty much dictate what price they will pay as long as it doesn't drive the providers directly out of business. But it is disingenuous for OP to suggest that because taxes go up it is an overall worse situation for those paying those taxes, implying there is no way they would save money.