Buteyko practioners build up the ability to work very hard while only nasal breathing over the long term. The point is to learn to modulate breathing in a way that keeps a certain kind of blood chemistry (CO2 levels) and cellular oxygenation.

If you commit to nasal breathing for exercise as a constraint, it does force you to modulate your exertion while also increasing your CO2 and developing, according to the Buteyko folks, a new baseline for respiratory health and capability.

If you're running for your life from a tsunami, by all means mouth breathe. If your purpose is maximum exertion, of course mouth breathe. But that's not the only possible purpose of exercise. It can also be about respiratory training. Nasal breathing becomes a natural guideline/modulator for long term improvement in that regard.