This reasoning doesn’t hold up to scrutiny .
Gains and losses in spending really don’t balance in the simplistic way you seem to be suggesting. It is completely possible to invest money in good , effective care and health systems that result in a win win situation for patients. This then results in huge economic savings as well as optimal health outcomes .
Some examples -antibiotics are still hugely & inappropriately prescribed. Also the air quality & hygiene levels in NHS hospitals are too often suboptimal .
These factors lead to iatrogenic illnesses and death through ( eg) MRSA , Sepsis and hospital acquired pneumonia.
Prescribing antibiotics in accordance with proper clinical indication and adhering to proper hygiene protocols , together with excellent air filtration systems would both SAVE money and many lives .