But, perhaps, not as much as treating those people in ERs.

No - it will be more. Treating people in ER's is pretty expensive for what you're treating - but giving people all the health care that normally gets covered under insurance ends up being a whole lot more. A ton more. Because an enormous amount of health care coverage doesn't qualify for ER coverage. And it's been a really long time since I looked at it, but my recollection was that studies found that ER usage was mostly unaffected by health care expansions to the uninsured.

Because the patients don't eventually get care. That's why it's bad for the people who are uninsured to be uninsured. To use your example, it's really expensive for the government to provide free oil changes to everyone. And they're not going to pay to fix the engine when it throws a rod, then the government doesn't save any money by paying for the oil changes. It's just really really bad for the people whose engines are no longer usable.

Very few preventative care interventions will end up reducing total long term health care costs. There are a few, but most have not been shown to do that:

Are there policies that can both improve health and reduce health care spending in the long run? Is it possible to improve health for free? The answer is occasionally yes, but only in a very limited set of interventions, such as colonoscopy for 60- to 64-year-old men or childhood vaccinations, where the downstream reduction in health care spending more than pays for the intervention itself.1

jamanetwork.com - Jama health forum

Basic health care is the cheapest way of providing good health, but that is not the same thing as saying that the dollar cost of the preventative health care is lower than the downstream savings on medical interventions later.