My current take; having been a convinced triple-a-holic until I built a compact equipped bike, because I could;
Compact large ring; riding on the flat, going downhill.
Compact small ring, going uphill
Three shift at back = one shift at front = broad equivalence of gearing is a useful rule of thumb.
Shifting front and rear simultaneously a useful, and satisfying skill.
Triple only needed for lugging luggage or at the end of very very long rides at the limits of my fitness/endurance that involve one more range of hills before home.
but then the my current liking for compact came after an extended period of riding only fixed, and occasionally ss, which made me realise much of my need for a wide range of gears was mental not physical.