There is a fundamental difference between reducing costs and simply shifting costs around, like a pea in a shell game at a carnival. Costs are not reduced simply because you pay less at a doctor's office and more in taxes-- or more in insurance premiums, or more in higher prices for other goods and services that you buy, because the government has put the costs on businesses that pass those costs on to you.
Costs are not reduced simply because you don't pay them. It would undoubtedly be cheaper for me to do without the medications that keep me alive and more vigorous in my old age than people of a similar age were in generations past.
Letting old people die would undoubtedly be cheaper than keeping them alive-- but that does not mean that the costs have gone down. It just means that we refuse to pay the costs. Instead, we pay the consequences. There is no free lunch.