The Wim Hof method unfolds its health effects by hormetic stressors, respiratory alkalosis is one of them (a minor one). The WHM does not follow the pH theory, even though Wim himself gave ambiguous statements in older interviews about this. There are many people who misinterpret the WHM breath work as plain hyperventilation, which is very wrong. It involves a hyperventilation phase in preparation of a hypoventilation phase. This is similar to apnea protocols. The hyperventilation phase itself can mediate minor health effects. As it is not a chronic practice but relates to a few minutes per day, the stress of respiratory alkalosis is very likely within the hormetic range, hence beneficial. The WHM does NOT advocate continuous hyperventilation, which is known to be linked to chronic disease (exceeding the hormetic window).
The clinical trials of the WHM are peer reviewed and well conducted. However, people tend to mix Wim's interviews with the clinical evidence, which is obviously bad. The major paper (group study with control group) is this one: https://www.pnas.org/content/111/20/7379.full.pdf
It clearly shows the anti-inflammatory effects and increased leukocytosis of the breath work (intermittent hypoxia) and also shows that blood pH correlates to the respiratory rate, more precisely blood CO2 levels as expected. Those are normal blood gas dynamics, nothing woo woo pH stuff and no serious scientist would attribute the health effects of the method to the temporary blood pH fluctuations seen from a short hyperventilation phase, especially not when far more dominant and better documented effects on hormonal adaptations can be discussed instead. Some practitioners get quite enthusiastic about urine pH measurements, which are VERY high after the breath work, however all this indicates is normal kidney function in response to temporary respiratory alkalosis, nothing fancy at all. The body increases bicarbonate outlet via the kidneys (renal compensation) when blood CO2 gets too low (hyperventilation) to maintain blood pH homeostasis. the pH strips measure this bicarbonate. Another misconception is that the reading would correlate to progress or health, while it actually just correlates with hyperventilation intensity/duration. It is quite annoying how many misconceptions about simple physiological details float around the web, primarily due to the success of the pseudoscientific pH theory and alkaline diet. I guess some people just got rich with that crap...
Understanding the WHM means understanding hormesis and the stress response in the first place. The whole idea is comparable to physical exercise: stress the body enough to become stronger but not so much to take damage.