> you will miss quite a lot of valuable things
Arguably, the lack of medical evidence tells us that this is in fact not a valuable thing.
Absence of evidence is not evidence of absence. So yes, extremely arguable indeed
> the lack of medical evidence tells us that this is in fact not a valuable thing
Except almost none of the most valuable things I've encountered in life had any convincing medical evidence I could find beforehand.
I am an academic scientist that designs and reviews studies all day long, so I am very steeped in the practicalities and limitations of biomedical research, and as such have completely lost any illusion that biomedical research is in a state where it can guide most of my personal decisions in a useful way- maybe it will be someday. There are many things I know about as a scientist, but can't get funding to study or publish on because the funding agencies don't care about them, and/or there are practical constraints that make it impractical to study.
If all of your personal decisions are guided by peer reviewed literature in it's current state, you'll probably be sicker, and have an empty dull life compared to someone that just uses common sense, tries things, and pays attention. I say this from having seen it happen many times in the biohacking community, the people most steeped in attempting to translate research into life decisions often died young, or even got to be one of the only modern people to experience diseases of malnutrition.
For one, you have to pretty much assume there is some specific benefit you can physically quantify, and that it will apply to almost everyone in your study population, both very unlikely to be true in cases like studying breathwork.
For example, I'm a person that tends to be pretty uptight and overstressed, what you might assume in scientific terms is "sympathetic activation"- and there is a lot of breathwork research showing that almost anything that has an extended exhale can shift you into parasympathetic activation, where you calm down and relax. There is lots of research on this, and it arguably covers Buteyko, but they won't use that term in the article title, because it's more general than just Buteyko alone.
Now, I don't need some peer reviewed study to just try Buteyko for a few minutes, and immediately feel calm and relaxed, and see that I can suddenly notice the colors around me, and feel joy, when I couldn't before. If a massive peer reviewed study proved to me that this does not happen to most, or even any other people except me, why would I care about that at all? Does it mean I shouldn't do it? What if I have a problem not enough of those people have to make it show up in the statistical analysis, or my body responds in a way most of theirs do not?
There are huge limits to how meaningfully you can generalize from scientific studies about populations of other people, to yourself. Moreover, you have to choose up front what outcomes or effects you will look at in a study, and if our biological understanding can't even guess at the outcome that would have been useful to look at, the study is doomed to miss everything.
Sit down, and try it- or don't, but don't assume you can learn ahead of time if it will be worthwhile or not for you personally by looking on Google Scholar.
There may be evidence, but there may not be a peer reviewed study of the evidence.
Medical evidence costs money. What would look convincing costs sums few can pay. If you use only that medicine you basically use only Big Pharma. And they are set to produce only specific type of medicine: something you have to buy, preferably for life. A breathing technique is not like that so it will never amass that much "proof".