The amount of tickets released for each show in the days leading up to the performance is much more than required to be held back, so this scheme is quite obvious.
I'm not sure the scheme is even half as obvious, let alone nefarious, as you seem to think... It's an extremely well-reviewed transfer from London, by a major playwright, playing a limited 7-week run at a relatively tiny off-Broadway theatre. On top of that, the run is exactly coinciding with awards season in Hollywood, where said playwright's new film is not only right in the running (it's already won Best Picture from the Golden Globe and Critic's Choice awards), but is currently (as of today, Jan. 19th) the #1 odds-on favorite at Gold Derby website to win Best Picture, Best Actress and Best Supporting Actor.
Tickets went onsale to the public back in October, and for subscribers well before that. By the time I purchased seats a day or so after they went onsale, a lot of good seats were indeed gone but there were still plenty left. Family and friends who I alerted to it, however, said there were already slim pickings a few weeks later, even before "Three BIllboards" was released in November. If the theatre has held back some seats (as I'm sure they have), then it's possible you'll see a few scattered seats made available - and yes, probably for premium prices - throughout the run. But anyone who's surprised that the show is basically sold out at this point, let alone thinks it's all part of a grand conspiracy, is a bit of a fool, I'm afraid.