The Pirate Bay and other torrent networks were built by people with a passion for building, maintaining and hacking things. People who, even without a solid CS background, would spend hours a day learning new things, developing distributed protocols, evading DNS blocks and hosting their content wherever they could to make it accessible - included the small server in their own garage if needed. And they are used by people who don't mind learning a new protocol or how to use a new client to get the content they want.
I don't see the same amount of passion for technology and hacking among the Parler users, nor its maintainers. Those who believe in conspiracy content are people characterized by a psychological tendency to take shortcuts whenever they can in order to minimize their efforts in learning and understanding new things. So when the first blocker hits they usually can't see alternative solutions, because it's not the way their brains are wired. They always expect somebody else to come up with solutions for them, and they always blame somebody else when the solution won't come. And even if they decided to migrate their content to the dark web or on a Tor network, not many people will follow them - both because they don't have the skills, and because they don't want to acquire those skills. Plus, they'd lose the "viral network effect" that they get when posting click-bait content on public networks, the new censorship-proof network will only attract a small bunch of already radicalized people.
And even if they wanted to hire some smart engineers to do the job for them, we all know that engineers tend to swing on the other opposite of the ideological spectrum. Those who have built systems for escaping REAL authoritarian censorship would rightfully feel disgusted if asked to apply their knowledge to provide a safe harbour for rednecks to vomit their conspiracy-theories-fueled hate.