All good points.
I only have a hunch about the romantic entanglements on the show, and that hunch is that Sorkin probably hates writing them, so he sort of phones that in. He may be a great writer, but I think he has an ego to match, and figures he can whip off that stuff without even breathing hard and still have it better than what most other writers would labor over, but then that of course dilutes it into stuff not that far above, or maybe not above at all, romantic stuff written by writers who love to write that kind of stuff, even if they are not quite in Sorkin's league.
Robert and Michelle King over at The Good Wife come to mind, because the romantic aspects of that show are up to the level of the palace intrigue, political machinations, and core story of Alicia Florek dealing with her world, all of which are top-shelf. They seem to take great care in all parts of the script, and are very skilled in that endeavor. They can write an entire script, and in fact 22 entire scripts per season, and not have one line or one scene be uninteresting, or have it be so "Sorkin-like" that it causes some members of the audience to howl or take to Twitter to register their complaints.
By comparison, Sorkin, who has plenty of detractors, is a shooting star who when writing about what he cares about has no peers whatsoever, but when adding in the stuff he doesn't really care for he phones it in between yawns, and we as viewers just have to tolerate it, power through it until the next mind-bendingly brilliant nugget about what Sorkin really wants to write about appears in the next scene, which is usually worth the trip.
IOW, when they pitched this show, the suits at HBO while officially hands-off, giving carte blanche, and taking a no-tinkering position, very likely convinced Sorkin and Co. that HBO would probably balk at a show that was just about the procedural aspect of a news organization that had a political tone, and urged him to shoehorn stuff into the show that would make it also a soap opera that would broaden its appeal to the great unwashed. And I think he capitulated to get green-lighted. Which also may be why he is ready to move on after 36 episodes.
Bottom line, as a compromise, in his writer workflow Sorkin blasts quickly, maybe even unconsciously, through a few romantic scenes as capitulation to what the suits want, just so he can also really concentrate on blowing us away with the stuff he really cares about. He may be even thinking about the scenes and lines he cares about at the very same time he is churning out the romantic scenes on autopilot.
The reason I think this is not all that far-fetched is because that is exactly how most brilliant geniuses think and behave. Mercurial, of course. Unpredictable? Not so much.
Again, just a hunch.