They weren’t that rare or expensive. Side-changing machines were quite common once digital sound was introduced in the late 80s; Pioneer kept one or two single-side players in their line-up at any given time as entry-level players, but those into LD tended to drop a lot of money into the format, including on the players. I’d estimate roughly 50% of all machines are side-changing, with a majority of those sold after 1988 being side-changers.
The feature you mention afterward-- still frame-- is what tended to denote the expensive machines. The effects available on machines with digital frame memory were fun; not just still-frame on pause on CLV discs, but with a jog dial, one could spin the picture back and forth at any desired rate of speed. Side-changing machines with digital effects could even make the side change almost seamless… cheap machines would take a few seconds of black screen to stop the disc, spin up backwards, and flip the laser assembly to start side 2, while high-end machines could achieve this while playing out the last bit of side 1.
Anyway, I can’t find my last few copies of the Laser Video Guide, so all of this this comes from memory, but addressing the OP: at the peak of LD, right around 1994 or so, Pioneer announced something like 5 million LD players shipped and sold in the US. Sounds impressive until you realize that they were pretty much counting all players ever sold (possibly including even DiscoVision players from 1979 on!), that all machines sold before 1986 were unable to play digital audio and were essentially obsolete, and that the core of the LD market tended to own multiple machines. Heck, I was a poor HS drop-out, and I had three machines then.
A more realistic assessment for market penetration is cited in the Wikipedia article on LD-- around 2 million households in the US. I’ve also seen similar numbers for Japan (higher percentage market penetration, obviously), and around 500,000 for Hong Kong. Europe’s market was smaller, in the low hundreds of thousands-- LD was engineered around NTSC, and didn’t fare as well with other standards.
Individual titles really didn’t sell in numbers that would seem impressive. Again, going from memory, one of my LD magazines was jubilant at sales of ~25,000 on some title (I think it was Akira), once again at the peak of LD, before DVD was announced as forthcoming. The LD market consisted of the early adopters of DVD; once DVD came out, LD sales dropped to nearly nothing in the span of a few weeks. New titles became available only to pre-orders through Ken Crane’s (owned by Image Entertainment), and movies would be cancelled if they didn’t hit 500 orders. I’ve mentioned it before, but when a remastered Indiana Jones trilogy couldn’t manage to find 500 buyers when it wasn’t available on DVD, and it was known that it wouldn’t be for some time and got cancelled, it was obvious that LD was dead.