Essentially, you have the answer already. Since actual Nazis are still very much a highly relevant cultural reference, there is not yet enough inertia for Nazi to become a generic term. Conversely, since few care about Italian fascism, the need is not felt.

The difference here is that this is not something that an intervention can fix, unless it could somehow compete with decades of cultural interactions and signifiers from billions of people. It's not a case of containing anything: that's essentially an anthropomorphization similar to seeing evolution as having intent. That is why the idea of wanting to educate people in the hopes of enforcing "correct" wording is fundamentally flawed because it has almost nothing to do with how words actually change or stay the same.