No, it wouldn't. Fixed function hardware is efficient, yes. But compression algorithms tend to evolve over time, especially on PC. E.g. LZ or kraken are nice, but even they evolve and when that happens, the fixed function hardware is useless. You can do something like that in a closed environment like consoles but on PCs it just don't makes sense. PCs can be upgraded with faster CPUs, more cores, ... that can do the work needed. Yes it is a bit brute-forcing through the stuff, but at least you can always use what is best for the situation and always use the newest stuff.And moving everything to the CPU via dedicated fixed function hardware would be a better option as it would offer a more efficient approach.
It is a bit different with things like tensor cores (or something like that). Those are not really fixed function units, but good at one thing and bad at other things. I guess we might see something like this in future, just accelerate compression. Some general purpose cores that are especially fast with de/compression stuff.
This compression thing somehow reminds me at the early Q2/3 engine games that had compressed files to save bandwidth but as the bandwidth of the HDDs grew over time, it was faster to decompress all files and directly to use those.