No, you're not quite understanding what ActivityPub is. The data under all the fediverse services is not the same infrastructure at all. The communication between those various services just uses the same language (ActivityPub). Those various services can interpret and store (or ignore) ActivityPub messages any way they want. Service instances add another layer to the whole thing as well.
In order for an "everything app" to be successful (if you buy the argument that it feasibly can be), it would have to be a centralized service. Decentralization, by its very nature, encourages the opposite of that -- want to make some niche service because existing services don't satisfy some fringe need you have, but still want to interact with others on other platforms? You can do that with the fediverse. But that also means your new service isn't part of an "everything app"... it just can potentially talk to one that might exist.