They stick with "democracy" because the only republic they know is the people's republic, and that phrase evokes the truth of their evil.
It reminds me of when the German-American Bund had their big shindig in Manhattan Square Garden in 1939, and hung a huge full-body portrait of George Washington next to a huge swastika banner, as if to conflate the two. What is scary is that there were enough people who thought the two were equivalent; what causes some optimism is that the overwhelming majority of Americans knew better, just as they know better about Dark Brandon today.