If we're all unhealthy, then that will save the taxpayer money rather than cost the taxpayer. Dementia is the biggest health expense at present, and dementia is suffered very much more by thin, healthy people than by fat, unhealthy people. Why? Because the biggest causative factor in dementia is growing old; and fat people die younger so are less likely to get it.
Fat people, a recent survey says, cost £600 per year to the NHS more than thin people. I don't doubt it. But that's only when they're alive. When the fat person has died and is costing nothing, the thin person lives on drawing pensions, nursing home fees, and continued medical expenses. Fact of life - we will all die, and most of us will die of something expensive. A healthy lifestyle just delays it.