It was interesting to hear anecdotally, via this board, that the She Loves Me cinema screening audiences were quite small, despite that having been a much more acclaimed production. The livestream option might have had an effect there though (and that strategy might be working out better financially overall).
I'm guessing that there's a bit of a chicken-and-egg problem in terms of raising interest about these screenings. An average, not-rich, time-poor person who doesn't live within easy distance of New York, has little reason to keep up with Broadway happenings and get interested in new productions he/she assumes he/she will never get to see (or, not until a possibly-mediocre tour many years into the future or whatever). (We happy few long-distance fans are the exception.) So he/she is not likely to feel any spark of recognition or excitement upon first hearing that some Broadway show called 'Allegiance' is getting cinema screenings. If wider distribution of Broadway shows became much more frequent and widespread (in terms of more productions getting recorded), then more of the general public might gradually start to think it worth their while to cultivate an interest in current Broadway productions, so there would be a larger pre-existing market for these screenings. But, that would first require heaps of shows to endure less-than-profitable recordings and screenings in order to establish the screenings as a common occurrence. Not likely. There's also the fact that a lot of the well-known shows, are well-known because there's already a decent movie adaptation available.
I also remember hearing an interview with a cast recording company executive (possibly Kurt Deutsch?) who said that the profitability of cast recordings comes over a longer stretch of time these days, as new people here and there discover the show via a local production and seek out the original cast recording many years after it was released. There may have been some spin there, but he might have a point. Maybe a long-term model (eg, BroadwayHD or DVD releases) is generally going to work better than trying to drum up awareness 'out of nowhere' for a one-off or two-off cinema screening.