There's an interesting question about what happens if the site goes down and what that means for the people who find themselves persons of interest here.
The kiwifarms exists because the man at the helm is too stubborn for his own good and has the necessary skills to keep the ship afloat, even in the face of hardship and headache. It's for that reason that I can't see a singular successor reaching the size of the farms. This obviously leads people to believe that all you need to do is cut off the head of the dragon and then then the village we call the Internet can be free from this menace. The problem is that this isn't a dragon, it's a hydra, cut off one head and another 2 grow in its place.
Something like the kiwifarms will always exist but the nature of that successor would probably be very different. The modern Internet has made it hard to discuss distasteful people or subjects or even just to discuss in an offensive manner. But while the Internet has changed, Human nature has not. We didn't invent the concept of schadenfreude or gosip and people.
What would the future look like then? I feel like any forum would be heavily focused on a particular individual like DSP, Ralph, ect. These would be both easier to maintain and much smaller, allowing them to fly under the radar. They probably wouldn't be as resilient as the kiwifarms has been, but I think the traditional forum is probably on it's way out. I think it's more likely that Discords and other similar services will probably take over as the dominant form any kiwifarms inheritor takes.
The large and open nature of the kiwifarms and concerns about it's legality keeps many of the bad actors at bay. That's something of an idealised version as there are absolutely unsavory individuals and echo chambers here but it would be far worse without the farms.