The idea of using statistics to determine whether a course of treatment is better than another is a "modern" concept. Epidemiology and statistics seem obvious to us today because we have been raised with them. They were not obvious and required "invention."

In any case, as you may know, determining whether a course of treatment is or isn't effective is actually non-trivial if you are serious about it. You need controls, you need a sense of how to evaluate and remove sources of error and bias, you need to know how to estimate the effects of random chance. These are 19th and 20th century techniques. We still debate how to improve them today and we have many modern instances of uncertainty about whether treatments work or not (and we have deeper understandings into the ways in which things like the placebo effect make determining efficacy very difficult).

Separately, it is also worth noting that the premodern conceptions of how to think about mathematical, philosophical/religious, and natural knowledge are not the ones we use today. Mathematics even up to the time of Galileo was considered to have limited applications to the natural world. Even in the time of Boyle and Hobbes there were deep debates about the value of deductive versus inductive reasoning as a means of determining truth. The more one reads about how very smart people in the past thought about how you create knowledge, what kind of knowledge exists, what kinds of natural phenomena can be subjected to these kinds of treatments, the more you realize how alien the past is, how different their mindsets were than our own, and how much what we take for granted is the product of centuries of sustained thought about what it means to know the world. Science is not a natural mode of operation.

Separately (again), especially in the medial realm, but really in all observational science, what you think is a "relevant" symptom or relevant treatment or how to evaluate progress, etc., all varies on what your underlying theories of illness are. Even John Snow's famous cholera-is-waterborne conclusion, today seen as one of the hallmarks of statistical epidemiology, took a generation to really affect medical practice, because it went so much against their assumptions about how medical illnesses worked and how cholera in particular worked. Consider how long it took people in the past to realize that external sources of contamination were what were causing so many infection deaths from surgery — this seems patently obvious to us today, because we have already internalized the idea that bacteria exist and are everywhere. Germ theory is in fact non-obvious and took a lot of careful work, even as recently as the 19th century, to develop. It took at least one generation for people to start believing in it intuitively.

We also have plenty of evidence in modern times of people thinking they have understood a good course of treatment and later learning they have not. The guy who invented the lobotomy was awarded a Nobel Prize in Medicine in 1949. And yet today we would hardly call that one of medicine's great surgical innovations.

A good place to start in thinking about why people in the past see things so differently than we do today is Kuhn's seminal Structure of Scientific Revolutions. On the invention of statistics, Hacking's The Taming of Chance is excellent and does a great job of explicating the "work" that the development of statistical and epidemiological thinking requires.

I'll preface this by saying I don't have an answer.

The problem with asking "why not" rather than "why" is that we don't know why not. There's never any documents that say "we didn't try better idea A because of whatever reason."

Asking about something we apply in our modern world is especially problematic because our hindsight is always 20/20. With the knowledge we have now, of course we should assume that the scientific method is best. And the old world did have something like this, Epicurus knew it, but there's no way we can possibly assert with any confidence why they didn't want to apply this to medicine.