Sledgehammer and other smashing becomes much more useful outside of combat, heavier vehicles can be worked on without jacks, and all melee attacks become stronger, and more carry weight, and improved HP… and stamina? Are the advantages to high str stat that come to mind.
My suggestion: use that high str to sledgehammer your way into bank vaults, military bunkers, armored lab areas and the like. Though you probably want to bring and armored sled with you to hide behind if you expect turrets.