It doesn't have to be mainly focused on it, but it should at least have moments where you can feel the relationship is believable for certain characters if they are being paired up in the end.
Can't say romance isn't important. It's that fighting games suck at this department when it comes to making a good one (they kinda do). It's whether or not it's worth doing into making one. For the general case, if the romance is a poorly written one, then it would be time consuming continuing it or just coming up with one when they can use resources or writing space for something general.
I do think FGs could improve on it, but if it creates nothing but poorly written dialogue or useless hints that only extends one's patience, then I'd probably recommend an entirely different video game genre when it comes to any sorts of romance.
Well Fighting Games aren't the only genre about this factor, but for that genre it's not very story based and most companies want the keep the characters single anyway (Most notably Capcom) . Which is why we don't see someone like Ryu or Chun li end up with someone else. Or it would be the situation like the time that suddenly Kazuya and Jun, sort of, got together and had Jin because....Next Generation for Tekken 3?