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Sure, if you're making up all the rules you can make up all the rules. Matter could be composed of the body of a dead god, for example.
Whatever rules you make up must be consistent with macroscopic observation, though. So if you postulate that matter is formed from the flesh of a dead god, you still need to prove that it doesn’t need to quiver.
Why would it need to quiver?
To contain the arrows of time and entropy, obviously.
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.