Computational sampling suggests that the non-ordinary locus and several other p-rank strata of hyperelliptic moduli are geometrically irreducible for all genera, with the p-rank 0 locus growing in complexity with the prime.
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Heuristics for (ir)reducibility of $p$-rank strata of the moduli space of hyperelliptic curves
Computational sampling suggests that the non-ordinary locus and several other p-rank strata of hyperelliptic moduli are geometrically irreducible for all genera, with the p-rank 0 locus growing in complexity with the prime.