I had the same question initially which has been extensively discussed elsewhere. Look at it this way. The only difference between a mute button and a true power button is you get a mute display on the screen. Just hit the home button on the console and the mute display goes away. That gets you to the same place.
I'm not sure why folks assume a power button would affect the display. We're talking about powering off the audio amp, not the screen.
You know, in thinking about this a little more, Mazda could simply relable the mute button on the console to say "audio power" and not display "mute" on the screen eliminating the need to hit the home button to access other screen functions. However, engineers are a literal bunch, and if we presume the audio amp is in fact always powered my suggestion would be a slight of hand deception even if transparant to the user. Enginners generally don't like doing that.
Why the audio amp is always powered up and whether it would matter if it wasn't might be interesting questions to answer but nothing I'd bother pursuing given hitting a home button is no particular inconvenience.