No this isn't the modern narrative, it's the stop gap solution for individuals that don't have the capacity to adapt to a new paradigm or have particular concerns (e.g. abuse)

The utility is still right there for whoever wants to take advantage of it, but they still have the option to forgo part or all of the trustless nature.

It doesn't matter if the "offending data" is sitting on a computer somewhere (that's all a blockchain is) what matters if it's accessible and as I mentioned, it's up to the blockchain nodes to transmit it or a user to consume it. Both of which can be solved if needed with middleware.