Before we get to the results, I want to highlight just why this is such a hard thing to study.

First – who do you compare the uninsured to? Like, what's the control group? If you compare uninsured people to those who get insurance due to disability or through Medicare, you might be stacking the deck against being insured – since that comparison group is a bit sicker than average. In contrast, if you compare uninsured people to people with employer-sponsored insurance, you might make being uninsured look worse than it really is due to the so-called "healthy worker effect". Accounting for these imperfect comparisons requires statistical adjustment, which can often be quite difficult.

Second – not all insurance is the same. The main mechanism by which insurance could save lives is through greater access to care (though, yes, perhaps there is some psychological benefit to just knowing you are insured, whether you use it or not). But not all insurance gives equal access to care.

Finally, if you're talking about mortality, the rates in adults are (fortunately) very low. That means to detect significant differences between uninsured and insured individuals you need a very large study.

What would be ideal is a randomized trial that took a bunch of uninsured people, gave some insurance, and left some uninsured. I mean, it would be ideal scientifically, maybe not ethically.

Actually, this happened in Oregon when the state held a lottery for Medicaid slots.