The economic textbook lists market failures, but the public has their own much less well thought out list of what they think are market failures.
One public version of market failure is called "Needs". For some reason, they think that if something is important that means government should do it. Of course, if government is better at doing important things, then why wouldn't it be better at doing unimportant things too? Why shouldn't government do everything? It seems like the assumption is that governments are just more reliable, which is generally untrue. If it were true, then why wouldn't we just always depend on the more reliable mechanism?
Demand curves slope downward, and it's not like demand reaches a threshold beyond which something becomes a need and now economics works differently. If something really is a need then markets will produce enough of it that it will be cheap and accessible. If markets can't do that because something is scarce or hard to produce, then there's nothing magic about government that can fix that problem. Lots of people need a cure for cancer, but we don't have to resort to vague conspiracy theories to explain why we don't have one. Cancer is just really hard to cure. Can you really believe that someone couldn't make a lot of money selling a cure for cancer? Can you really believe that sick people are willing to pay more for treatments for cancer than a cure?
If we look around we will notice markets producing lots of needs; toilet paper, gasoline, and groceries for example. I would probably spend a significant portion of my income on toilet paper if I had to, but I don' t have to because normal market mechanisms keep the price low. It's untrue that producers can sell at whatever price they want because we need what they produce.
Some needs aren't produced very well, but that's not because they're needs and therefore markets can't be trusted, but because of some other market failure. Lots of economists think health care should be produced by governments, none of them think that it's because health care is important.