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To explain any macroscopic effects that necessarily depend on matter waves. If there are any. Which is my question.
This is a pretty difficult question to answer since all phenomena are quantum. A star is powered by nuclear (quantum) fusion. Permanent magnets depend on the quantized angular momentum of electrons. Could these phenomena be allowed by something other than quantum mechanics? Maybe. But a constant goal of science is to find the simplest explanation for all we observe, meaning that whatever alternative explanations you come up with, should they be correct, then taking them all together will constitute a theory that at least looks an awful lot like matter waves (mathematically, at least).
Superconductors and Bose-Einstein condensates are both macroscopic phenomena that result from coherent matter waves.
Maybe there aren't any in our conceptual universe.