I guess I always took the phrase "unreasonable effectiveness" to refer to the "coincidence" you mention in your reply.

Unreasonable effectiveness tends to refer to the observation that the same mathematical tools, like, say, mathematical analysis, end up useful for modeling very disparate phenomena. In a more basic form it is "why do mathematical ideas help us understand the world so well?". The answer suggested in the OP is that the question is a tautology: math is a meta-model build by human minds, not a collection of some abstract objects which humans discover in their pursuit of better models of the world. The JPEG analogy is that asking why math is unreasonably effective in constructing disparate (lossy) models is like asking why the JPEG algorithm is unreasonably effective in lossy compression of disparate images.

The "coincidence" part referred to something else: that pursuing math research for its own sake may occasionally work out ot be useful for modeling the physical world, number theory and encryption being the standard example.

As a pure mathematician, I never think about applying a tool to the real world, but I do think I'm working towards a very compressed understanding of tool making.

When I talk to someone who works in pure math, they usually describe the motivation for what they do in almost artistic terms, not caring whether what they do can be useful for anything, so "tool making" does not seem like the right term.