We had a section like that on the site before, as WaveVelour pointed out. Instead of plot or story based, it was non-sexual. There's a distinction there, but they served fundamentally the same role, although they don't technically. I don't think it was very active. Whether or not a section of the forum is active or not should not necessarily determine if it should be omitted from the forum. There may still be some people that use it at some point, and there isn't much harm in it being around. At worst it'll make the site look more dead than it actually is if there are sections of the forum with very little to no activity.
That being said, I don't think that it's a particularly good idea. It sends a message the rest of the forum isn't about writing, but is instead about smut. It propagates the idea that it's a meat-market and is intended for people to find "hawt virtual fuk". I've always seen BMR as a message board for adults to role-play, where they are free to play what they want. It just so happens that the popular thing is a whole lot of smutty and porn-centric writing.
I feel a much better solution would be filtering and search enhancements, but I understand how that can be difficult to implement.
An easier implementation would be the previously mentioned section specifically for off-site role-playing. That will attract the attention of many people that are just looking for smut and cybering. Let them all have their own pit to roll around in if that's what they want. I don't think it will be effective, because it would just allow those people to cast a wider net and give them more search threads.
A more extreme step would be to rebrand the site entirely by sectioning of a specific subforum for erotic role-play. It'll then be understood that BMR is a website for general role-playing and writing, but it does have an area for erotic and sexual oriented content. This avoids the problem of the website being seen as smut first, and might encourage more writers that are interested in writing instead of getting off to come out of the wood work. The main role-playing parts of the forum would then be, at least loosely, enforced as non-sexual.
Then again, it might achieve absolutely nothing. I've been on websites where sexual content was prohibited, but once things moved to PMs then the façade was dropped. There is still nothing stopping people from posting in every section of the site with somewhat modified threads, all with the intention of guiding the role-play in the direction they want. That might sound stupid and inefficient, but I'm sure the staff here can tell you all about how many of the users here act and what they try to get away with.
A bigger problem then emerges. Are we then going to police what constitutes a "story and plot" role-play versus a role-play that is just smut? Someone else in this thread brought up that it's quite possible to have a very smutty role-play that plays to story and plot quite well. The two things are not mutually exclusive, and you can have your cake and eat it too. Sure the staff can certainly be the arbiter of what is and isn't story and plot based, but that starts to sound super controlling to me. I feel like most people like BMR, because it's relaxed and relatively safe with good staffing. Nobody is judging you and putting a leash on what you can play, with exception to the very lenient and reasonable rules. Nobody is told they can't make a search thread somewhere, because they don't live up to some arbitrary and subjective standard.
What's the ratio of smut to plot that puts smut on the back seat? How do you enforce something like that? Is there some kind of objective standard?
The only way I see this being done is if there is a section of the site dedicated to smut or erotic role-playing; and BMR is rebranded as writing and role-playing first, and adult role-playing second. In order to avoid subjective regulation of what is and isn't, the non-erotic part of the website would have to be specifically enforced as non-sexual. Then again, maybe the topic creator's idea will work out very well, and there isn't much of a discussion to be made. That just banks on the users of BMR using the site with all of that in mind. I'm just pessimistic and don't think it'll quite work out like that. I fully expect people to be sneaky and take advantage of the system in order to put out more request threads while still, essentially, seeking out the same thing.
Ask yourself, how many partners have you had that were seeking plot and story ended up disappointing you with quick jumps to smut? Happens to me all of the time.