Giving your creature indestructible can be a lifesaver if you need other stax pieces (I am assuming if you play Boromir, Warden of the Tower , you are playing a stax deck) to stay alive, or if you just want to beat down someone and survive a board wipe
Most of the time its used versus decks with x/1 creatures: Ragavan, Nimble Pilferer, Dragons Rage Channeler, Esper Sentinel, mana dorks, a Dwarf token, Inkmoth Nexus, etc
You hear someone ask Are you wearing jeans? to make sure Hurloon Wranglers denimwalk applies
Part of adapting to Play Boosters included making less unusable commons in Draft, which made the fifteenth card less necessary
At the most basic level, it can be a pseudo-protection spell by switching auras and equipment away from a creature thats about to die and suiting up something else