The existence of deposit insurance means that each unit of cash is worth less

If the Government is to give the banks deposit insurance, from the taxpayer, this will cause inflation because if the deposits are good for the payment of taxes then they will have value from the same source as the rest of the money supply. It is easier for people to pay their taxes, with the inflation and so the tax rates (in absolute quantities) go up and the old money is worth less than it was. It's easier for the Government to charge more as more people are able to pay, employers are able to pay higher wages and the old money buys less. The price of goods and services can be altered (increased) with the introduction of deposit insurance, not only the supply of base money, to get deflation we can remove this guarantee and watch the banks collapse.