I think there are projects before that do this. But I think they are not directly storing in bitcoin. There is a reason why signed messages are the only popular way. They have their own chain and I think the storage is encrypted in a way that is connected to their own chain. Most of the projects are in ETH before.
Yes there are some projects that I have heard of, they do want to replicate the concepts behind blockchain. I think data storage type of blockchain is a pretty helpful concept for data privacy if ever it comes to become created, being secured in cyber space will not be limited to using VMs, Tails OS, Deep Web and other privacy services, even the Surface web will be safe.