I think a romantic subplot can, if done right, add complex loyalties, depth to the characters and make some people care more about the characters. The problem is it's incredibly difficult to do such a subplot in a way that is really believable. As other people have pointed out, in real life, people do NOT show such feelings openly and immediately.
I tried adding one in my previous game, but frankly, it fell flat on its face. To keep the focus on the actual main plot (such as it was), I made sure NOT to focus on the romance, although I did have the 2 characters find each other "cute" at first and did have loyalties questioned and such. I attribute that to my lack of experience in game development and RL romance.
While it is true that people in the midst of a crisis can form deep, even romantic and sexual bonds very quickly, I don't think it justifies the Dulcinea Effect --- where the hero meets a girl and immediately falls so in love with her that he'll do anything to save her (see: Chrono Trigger among countless others).
To really do one well, the characters need to SHOW their feelings changing, but in real life we show that through subtle cues like facial expressions, changes in how we talk to someone (words AND voice tone/etc). So I think, unless there are a lot of very skillful voiceovers and cutscenes which show their feelings shifting, the romantic subplot is going to fall apart.
Then the developer has the difficult part of balancing this very-hard-to-do-well romantic subplot so it doesn't consume the entire game. This makes it even more difficult, since it requires a great deal of effort and cutscenes to do the subplot well.
In the RPGs I've played, I only felt FFIV really did a good job showing romantic involvement, and that was an established relationship (Cecil and Rosa). Well, it did a good job showing Edge's crush on Rydia as well, but there were no feelings developing beyond that, as far as I could tell.
Chrono Trigger, if it had a romantic subplot, it was news to me --- the Chrono/Marle relationship was almost entirely offstage, except for a few offhand comments and Marle's grief when Chrono dies --- but ALL other party members show grief there. Chrono being the Mute Male Protagonist doesn't help matters. I was quite surprised to see them marry in the end scenes.