I don't understand this. For my part, I've been involved in romantic plotlines from the beginning; my very first character, back in 1978, wound up in a politically advantageous marriage with the daughter of a high government official. I've had four PCs married to the characters of other players. (We won't mention the number of marriages and relationships I've had in LARPs and MMORPGs. I can't count that high.)
From the other side of the dice, a great deal of plot has stemmed from romantic entanglements. In my most recent groups, the only PC in one who wasn't romantically involved was a priest of a faith that preaches rigid monogamy. In the second, two PC aristocrats married each other to preempt their families from dynastic shenanigans. A key element in my wife's one-on-one sessions is the need to keep her young daughter relatively free of the risk of assassination.
A “distraction to the plot,” as many of the antis claim? Heck, any kind of roleplaying is. Characterization involves ties, bonds, limitations, phobias ... all that can get in the way of a mission. Why, people might be moved by a NPC's pleadings and act other than coldly or logically!
Damn, that leaves out likes, dislikes and character quirks, too. That moron who always insists on wearing red screws up the pattern-disruptive outfit. The fellow who likes cheap tobacco always smells of it, and that can tip off guard dogs. So you want to fight "honorably," blah blah blah ... screw that, just go and do the guy from behind, less risky that way. Every last little quirk is someone demanding some distracting center-stage time – even if it's but moments – to light up her pipe, recite a prayer over the bodies of the fallen, scritch his cat, grab her favorite pizza or read a few pages from a trashy novel during a lull on the stakeout. Ego stroking drama queens, the lot of them. Right?
In gaming groups mature enough to handle the subject (which I agree many aren't), romance is another aspect of the human condition, just as valid for PCs to explore and roleplay as any other. Strange though this might seem to some, not all campaigns are about nothing but the tactical resolution of problems set before the team.
You might ask, "What's the point of having a PC belong to a guild, if it'll only result in trouble - they want help, your status is imperiled, the chapterhouse burns down and they want money from you?" Why bother with the PC having a family, when family members only drag you down in like fashion? Why belong to a church, which only restricts your actions and movements, except in so far as your setting requires it to get clerical aid? Why be a military veteran, because the only time your ex-mates will ever show up is when they're in trouble? Why have neighborhood ties, because getting to know the kindly old priestess at St. Taria's or the tomato seller on the corner just means you're getting sucked into their problems?
And why is it that these questions generally aren't asked, not with one tenth the frequency of angry questions about "Why bother with SOs?" Why is it that ties and plothooks involving PCs are so much more tolerated when the dreaded "R" word isn't a factor?
We have a hobby with deeply misogynistic roots: one that stretched back to a day where rooms full of men and boys played wargames with lead miniatures. The games that stemmed from those were overwhelmingly based around tactical, statistical combat and nothing but. The problems set before the group to solve were dungeons, involving nothing beyond problem solving, tactical acumen, outguessing the Dungeon Master and dice luck. Players who could tell you in great detail that they "were" 8th level Lawful Good clerics with Wisdom 17, 36 hit points, Bracers of Wondrous Awesomeness and +3 Maces of Big Bad Smiting gave you blank looks when asked to name their hometowns, describe the clothing they wore or to expound on the doctrine of their deities ... when they'd bothered to name their deities at all, not always the case. The notion that roleplaying = acting wasn't common; third person "My character tells the NPC to back off" modes of speech were.
Quite aside from women not being welcome in that world – what stereotype of female players dominated the first decade of the hobby as heavily as the GM's Girlfriend, generally bored, mocked as incompetent and always marginalized? – romance and sexuality weren't either. Oh, sure, a lot of groups regularly patronized the local brothel ... along with locker room grunts and grins, and the dropping of a requisite few gold pieces. All suitably off-stage, with the (inevitably Frazettaesque-female) courtesans never seen or described, let alone named, extant only as part of some peculiar backslapping ritual affirming its participants as Manly Men.
And to a bunch of 14-year-old boys sitting around the table, clutching their dice, each concerned that they've never been laid and worried that they never will be, I'm willing to give a pass. But for everyone else?
Leaving aside those for whom gaming isn't roleplaying, and is solely about tactics, is there any more reason for sniggering than with any other type of plot, if you have a group not comprised of adolescent boys? Alright, let's get the 800 lb elephant out in the open and admit the secret fear lurking in the hearts of many gamers: that the (invariably male) PC having a serious relationship with the NPC (run by the invariably male GM) will carry a whiff of homosexuality.
(I'm quite serene with my stereotyping, because the number of these complaints coming from female players, with the exception of the I'm Freaking Tired Of His PC/NPC Trying To Get Into My Bodice riff, is about 1/100th those from male players.)
How to get past this, that's a question for which I don't have answers beyond an admittedly pompous and patronizing hope that more gamers just plain grow up.