Are you forgetting Edgar's line in WoR if you talk to him on the airship if he's not in your party? "If something was to happen to me, all the world's women would mourn"

Locke only makes those promises to Terra and Celes because he made a similar promise to Rachel, which he failed to keep. He's trying to make up for that failure by protecting Terra and Celes. So, to answer the question, Locke isn't a ladies' man, because there's only one woman for him.