They don't have the power to do that.
SCOTUS invalidated the core of the relevant law rendering it moot/unintelligible. It cannot stand as is; convention is that when part of a law is struck down the whole law is struck down unless otherwise specifically enacted with severance directives. The KY definition of “marriage” was eviscerated, leaving no definition of the word to act on.
Yes, SCOTUS very much has that power and exercises it often.