Travelling extended distances or multi-day hiking with no electricity in between. For example, when I did the Annapurna Trek in Nepal, I had the phone in flight (mostly no coverage anyway) and power save mode, so it'll last a few days.
But honestly, more airplanes, trains, coaches and airports now have power or usb plugs and if you go hiking, you can probably afford to carry a power pack, solar charger or invest in a dedicated device (e.g. Garmin).
it's not that an oversized 6.1" or 6.7" phone gives you double or tripple the battery time.
and if I go out for the evening and not carry a jacket or a bag, the mini has more than enough battery power to communicate with friends, look for and book trains and google maps me to the location while playing an audiobook during transit.