I think it depends on the definition of taking off. I see the Fediverse as a huge success with millions of people using it every day. At this point it's proven itself to be both viable and sustainable. I only see it growing going forward.
The Fediverse hasn't gone mainstream, but I think that's a different discussion. Fediverse primarily attracts people who are dissatisfied with the status quo for one reason or another. The existing mainstream platforms obviously work well enough, so there is no reason to expect average users to start migrating from them.