The point was how they gained absolute power, and I would also say that there were multiple factors at work, and I doubt that the GP meant that “abusing free speech” was the only method or reason, but was it not a factor at all? There is often so much “not this but that”, folks should consider “both-and”.

They gained absolute power through violence.

The Nazi party had a private paramilitary wing — https://en.wikipedia.org/wiki/Sturmabteilung — and political violence was both common and integral to their rise.

When the Enabling Act was deliberated and passed, giving Hitler effectively absolute power, Sturmabteilung paramilitary members were positioned both inside and outside the chamber.

That period of history was fraught with political violence enacted by people who claimed a moral imperative to curtail the freedoms of others.