Being relaxed is important in boxing too, if you don't stay loose and relaxed (other than snapping explosively when throwing a punch), it is easy to get fatigued quickly and also harder to slip or roll.
Yeah - I imagine that’s true for a ton of sports, but especially for any combat sport. I mean, even in shooting pistol (I shot sport pistol in college), breathing is the main thing you can control, and the main thing that will screw you.
The point is that staying relaxed in boxing during sparring or working the heavy bag feels counter-intuitive in the beginning. It seems like tensing up the core and arms would help punch harder, but you quickly learn that conserving stamina is more important than hitting as hard as you can (especially when starting) because otherwise you run out of gas pretty quickly.