There either is a viable market for 16mm printing or there isn’t and I’m speaking both of economic and cultural markets. If there is economic market demand, an entrepreneur will step in to fill the need.
Artistically cherished media without economic viability but with sufficient cultural demand may be supported by public and private institutions who step in and fill the gap between the two markets. But there’s plenty of competition for that support, and survival is often based on making the most compelling case. There’s increasing political pressure to take public money out of the equation, which will make the competition for private subsidies that much more fierce.
I first read Tacita Dean’s article with a sense that she felt entitled to have this service provided to her, but on re-reading I see that it is a heartfelt plea, and it is now up to supply and demand in the cultural preservation marketplace.
(I used to shoot 35mm 3D stills using a Stereo Realist camera, and have them processed and printed (irregular size prints for 35mm) through the local drugstore until they stopped doing it, then at the local camera store/lab, until they stopped doing it (and then they went out of business). I don’t have my own darkroom, so I’ve stopped doing that particular hobby.)