Isn't Gab exactly that? They seem to have "taken off" quite successfully among their own audience. Parler simply made a different choice wrt. whether to support interop and federation.
They were for a bit but they've defederated and the software is a huge mess. There are right wing free speech instances but they don't have any of the media attention.
It was right around the time congressional hearings were taking place about Twitter and FB suppressing conservative voices. A lot of conservative talk show hosts were talking about how they had moved to the platform and urging their listeners to do the same if they thought what Twitter and FB were doing was wrong.
When you have heavy weight talk show hosts pimping your product without paying them and they're touting your platform as one that doesn't censor speech, you're going to have a huge increase in followers.