Why is a just a rather odd wh -word. Its distribution is very limited -- it can only have the word reason as its antecedent, and since it's never the subject it's always deletable. Consequently it behaves strangely, as you and others point out.
Possibly relevant to why /z/ won: if I try to pronounce axis with a /z/ instead of an /s/, it sounds hardly at all different. Someone with a better understanding of phonetics can probably explain why the contrast is so small in that context.