I feel like this would encourage nothing but modding - there's already mods to change the sexuality of gender locked characters in multiple games, I wouldn't think adding more arbitrary gates would encourage different.
Personally, I wouldn't mind romanceable characters having more preferences, but the number of romanceable characters would have to rocket up. ESPECIALLY if you're going to put more locks that can't be changed after character creation, and don't want to lock people out of even the possibility of romance before the game even actually starts. And even if you've provided 2 or 3 options at the end of every possible gate-path, you'd still get people modding popular characters (or characters like Jack in ME, who have significant character moments only happen on-screen if you romance them) to be romanceable by PCs who can't, otherwise.
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Personally, I wouldn't mind romanceable characters having more preferences, but the number of romanceable characters would have to rocket up. ESPECIALLY if you're going to put more locks that can't be changed after character creation, and don't want to lock people out of even the possibility of romance before the game even actually starts. And even if you've provided 2 or 3 options at the end of every possible gate-path, you'd still get people modding popular characters (or characters like Jack in ME, who have significant character moments only happen on-screen if you romance them) to be romanceable by PCs who can't, otherwise.