when attempting to compress huge databases, it becomes worthwhile to build sophisticated computational tools into the compressor. And ultimately the development of these advanced tools is the real goal.

I don't see why thinking of the problem as a compression task will cast any light on the problem of building these advanced tools. Especially when, as you already pointed out in your examples, the concepts needed to build these tools are not discoverable from the data -- or at least, you are envisaging them as not being discovered from the data.