A common use case for this is things like car/plane instruments/nav/etc. You don't want that sucking power all the time when your vehicle is parked for 1 week or two, but you do want a quick transition from POR to usable UI up and running.

Hibernate has the disadvantage of needing a clean shutdown and increasing write cycles. You'd rather avoid the need to design for both. Additionally many embedded devices don't have perfect firmware and behave "weird" after a while (see planes needing a reboot every few months), which you'd extend over power cycles with this.