Wigner Functions are great and all, but they work quite badly for finite dimensional systems. Specifically they are a bit complicated for odd dimensional systems and don't work at all for even dimensional systems (see e.g. [1]). Given their limited applicability I don't see why we should treat them as particuarly fundamental when introducing quantum mechanics to students.

[1] https://arxiv.org/pdf/quant-ph/0507094.pdf