No idea where to find a good reading material. I will just throw here some random facts that I learned.

The health problems seem to follow a power law: there are many that can be healed for $100, relatively fewer that require $1000, etc., and at the other end of the curve there are problems that hypothetically could be cured if we spent the entire planet's GDP on them, but we are obviously not going to. That means, even in the ideal case, some people are going to die; we can only try not to make this number much larger than it needs to be.

On the side of the patients, there are some people who abuse the system and spend disproportionate amount of resources. There is a "Munchausen syndrome" and "Munchausen syndrome by proxy", a mental disorder where someone basically fakes an illness (for themselves, or for their children) and insists on that illness being cured medically... which is a waste of resources, and also makes the patient's health worse, and in an extreme case might even kill them. -- This is probably a huge problem, because there is a lot of trust involved in diagnosing. For example, if you tell the doctor "my stomach hurts, and I have been vomiting every day during the last week", the doctor will generally assume that it is true, and will try to figure out the possible cause (send you to various tests, try to prescribe medication, maybe even surgery if the medication does not make the reported symptoms go away), rather than suspect you of completely making this up. And of course, after learning about these mental problems, it is possible to update too much in the opposite direction, and dismiss patients' true reports, especially if they are of the kind "the patient reports being in pain, but all the tests we did seem okay". (Watch "Take Care of Maya" and "Sharp Objects" to get an idea how serious this is.)

From the signaling perspective, taking care of someone's health is a costly signal that you care about them. Which explains why people do it for many bad reasons. For example, people spend money on cures that clearly don't work or even make things worse, because being unwilling to spend money on cure seems like a horrible form of selfishness. The Munchausen syndrome is probably a way to extort sympathy (as a supposed ill person or a deeply caring parent of a supposedly ill child).

There are also people working under the simplistic assumption that "more is better", so when they have an actual illness, they will independently visit three or five doctors (without telling any of them that they did so) to get prescribed medication from each of them, and then they eat it all. That is a waste of resources and it damages their health. -- This seems to be less of a problem in the era of internet, but it requires centralized information, which needs to be balanced against privacy concerns.

Sometimes old people visit doctors just to have someone to talk to.

Then there are the economical problems about medical patents. The research and testing costs too much, because the government agencies want to err heavily on the side of safety. (As a result, for every person whose life was saved by preventing a dangerous medicine, probably many others die because a safe medicine was approved too late... or wasn't approved at all, because the approval process was too costly.) When the patents expire, the economical incentive is to forget about the existing medicine and invent a new one, perhaps 1% more efficient, but 1000x more expensive. Old pills are thrown away, because the producers have no economical incentive to find out whether it is safe or not to eat a 1 year old pill.

The threat of lawsuits also produces asymmetric incentives, especially in USA. Doctors send patients to needless tests which cost money and may slightly damage their health, just to avoid a possible question in front of the judge: "The patient died of X. Doctor, are you familiar with X? And did you test the patient for X?" So better test everyone on everything.

The health insurance in USA seems dysfunctional on many levels. I am not an expert on this, but it seems like it was a huge historical mistake to tie health insurance to employment. (It seems easier for a country that doesn't have health insurance at all to simply create it one day, than for a country where people with the best jobs have good health insurance and the poor folks have nothing to change this situation.)

The doctors work insane hours. This is partially self-imposed, collectively, because they try to prevent too many people entering medicine. Cartel behavior. On the other hand, there is the principal-agent problem: the doctors knows about medicine much more than you do, so if we switched to purely market system open for all, there would probably be too many charlatans? (We already have the homeopaths etc.) Also, if you have a serious medical problem, you need urgent help, and have no time to do research or compare options. So most of our assumptions about markets fail here.

Also, human health is complicated. Most doctors' knowledge seems seriously outdated, but it also seems unrealistic to do much better.