Earlier quoted context omitted.
Not only do they have significant value, but they're the only type of evidence you'll ever have for something like this - it's impossible, and almost certainly unethical - to run a randomized trial of keeping people from having health insurance. Also, while "Correlation is not causation" is, as you mentioned, a tired canard on the internet, people often seem to forget that all things that do have a causal relationshi…
Sorry, but no. 100 times no. Correlation is very often linked to a third factor or multiple factors which are not visible, nor measured in observational studies. Besides, let's not disregard the fact that correlation still has some good chance to be pure luck. Even correlation with 95% confidence statistical significance can be a random result in a non-nil number of times. So, no, you never prove anything nor imply a…
This is a totally unreasonable stance to take. You can't even imply anything at all with correlation? Really, nothing at all? It's no better than a random guess? Try actually doing some actual science with this attitude, and keep to it consistently, and let me know how far you make it. In fact, try the same thing with ordinary life, any kind of reality where your decisions have consequences in reality.