I know, one the one hand blaming NATO sounds like Russian propaganda, but on the other hand not blaming NATO puts the blame on Israel alone. On another hand(?!?) is it really NATO's fault? It's a clumsy way to refer to the member states, and it's not NATO that is supporting Israel, it's its members.

But your question was why not blame the Zionists, and IMO that's because Israel wouldn't be able to do this, if it wasn't for western politicians being afraid of being label antisemitic. Shifting focus to a broader perspective, and making sure people remember this, can potentially make people pressure their elected representatives shift their stance on Israel.

Israel would not exist without NATO backing it to the hilt.