I would say that the romances are important because it allows the player to act like a part of the in-game universe, to interact with the other characters in it. Without it, or without even friendship paths, well, Shepard wouldn't actually be a character, he/she would just be the player's avatar, as opposed to the avatar-character hybrid she/he is currently.
For example, the interactivity in Skyrim with many objects in houses and all across the game, the ability to lay down and sit in chairs and knock food and drinks across tables, was surprisingly fun to me, not used to being able to do that in game. Conversely, however, whichever character you choose to play as, (Argonian, Khajiit, Nord, etc) you are never really able to express any knowledge about the area you are in. Even if you are a Nord, if another character asks you if you know about the Dragonborn, there isn't any option to say, "Yeah, course I have." It is a necessity, of course, to inform players and depending on your character's race, it might not be known to them.
But like the very superficial interactions with companions, this does have the effect of making your character seem like an alien dropped down from the stars as opposed to a citizen of the world that would have to have some information about those around them.
I feel like character interaction, like romance, helps with that, makes Shepard less of an outsider, an interloper.