For genetic data, HapZipper beats general-purpose compression. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3488212/
So, yes, actively researched, but you've got to pick a specific task that makes sense. Even small niches are viable; I made a task-specific compressor to strip the essential numbers out of a remote sensor report to make it small enough to squirt to a satellite.
That's why people still write for the Z80: it's a fun toy.
It kinda didn't matter from 2010 on. But one area I've written my own specific "compression" methods in, for the last few years, has been in shipping data in and out of webworkers (in-browser or in Node). This is where there's still enough of a performance penalty on a lot of devices for sending 1MB that in use cases where you're spawning lots of workers to run long tasks, it makes sense to trade time to compression for a smaller transfer size.
https://blog.transitapp.com/how-we-shrank-our-trip-planner-t...
Eg. You work for a doorbell company and the boss says "yo, can we make our doorbell have 6 tunes instead of one, because our competitors are doing that. No, we don't want to change microcontroller".
Working on GPUs, I see many, and work on some task specific compression ideas as part of my job. The compiler has it’s own ways of compressing code & debug info. The hardware has it’s own ways of compressing textures. A recent feature we built on my team is a compressed encoding for adaptively subdividing curves. All of these things have the primary goal of reducing memory bandwidth, which in turn increases the speed of computation because memory is so frequently the main bottleneck.
Similarly, having to contain the decompression code in the measured result size and it being a relevant contribution is something that only applies in some use cases of compression.
I had to do this in the early '80s. The alternative was scrapping the boards and redesigning them to allow double the EPROM size but that would have been a lot more costly than writing the decompression routine and manually compressing the strings. It would also have delayed delivery.