I have been using a MacBook trough work for 7 years now and I think I actually clicked shutdown once this year too keep the battery at ~80% during my 1 month holiday. Otherwise I maybe reboot it once every month or two to fix some weird homebrew upgrade issues. And that's it. The thing is just "on" in deep sleep, forever.

If the Mac mini's behave similarly to the MacBooks, the standby energy usage is so low it's probably easier to just keep it in on/standby/sleep all the time and just wake it by keyboard or mouse. And because Apple develop their own hardware, standby and sleep actually work reliably. So they probably intend for you to only use that power button for a hard reset. Even shutting it down and moving it, plugging the power back in wil probably start it up again. Just like opening the lid on my shutdown MacBook also boots it before I even touch the power button. Even a keypress or mouseclick will probably turn the damn thing on.

Yes it's an odd design choice, but in regular day to day use it probably won't matter. Especially if you realise that its not a windows machine that needs to shutdown or reboot often.