> I’m not convinced breathing exercises by themselves do much good for physical health, but rather that good breathing habits are a consequence of overall good health.

The causality is clear at this point. Breathing and focus exercises like meditation are deadlifts for your brain. Like most other organs, it adapts to various stimuli.

If you're not convinced that breathing can affect your physiology or your mental state, try hyperventilating for a few minutes. I strongly advise stopping before you pass out.