This is true of health care too and was a major driving factor behind the ACA. If you (if everyone) goes in for a yearly or twice yearly checkup and health screening, then dangerous conditions like cancer, disease, injury, and so on get caught sooner. The sooner you catch a problem, the easier and cheaper it is to fix.

If you dont get regular screenings, then people find out they have cancer too late, usually after an emergency (an ER visit), when cost of care is very expensive. The ACA made the case that getting everyone more preventative care would reduce overall health costs.

Another factor is that hospitals do help the uninsured, then pass those costs along to the insured. There are so many hidden costs in our system due to cruelty and inefficiency that would go away if we had universal health care. But the key difference is that the current system funnels all the benefits/value (all the money) into the hands of a small number of people, while actually universal healthcare spreads the benefits out over all of society.