No other option? You can play Breath of the Wild on as many accounts as your heart desires to create with a different save file on each. You don't have to buy extra save slots, and certainly not "have to buy the entire game over again" as you imply.
I don't know how an XBOX ONE works, but on PS4 you can make separate user accounts as well and each user has their own separate save files. i'd imagine the experience is similar on X1. What you're describing for Breath of the Wild is also an option for Metal Gear Survive. The ability to buy additional save slots on the same account is a strict upgrade in comparison to Breath of the Wild...
4 ≈ One