What is special about a private blockchain based on proof of stake? I recently came across a paper published in 1988 called "A quorum-based commit and termination protocol for distributed database systems". I could not read it because it is not free, but to me this sounds very similar to what a private blockchain using proof of stake for consensus achieves. I have a hard time believing that's all there is to it considering all the hype going on. With that in mind, I have the following questions:  


Is chaining blocks together the only innovation here? Why not just have trusted validators sign transactions in permissioned distributed databases? We have had these technologies for decades. What is the difference?
Couldn't a 51% attack where someone has private keys for a certain transaction rebuild the chain from that point on for basically free? How does this achieve any realistic level of immutability?
Why would financial institutions want to 1. Pay to store competitors data 2. Allow competitors to see their data?


I want to understand what everyone is finding so new and exciting about private blockchains.
I have not read the paper, but here are some thoughts.   

Private blockchains make little sense (to me). But of course maybe a clever person will figure out a killer app for/on private blockchains. To me they are analogous to corporate intranets of the mid/late 90s. Those were hyped up as well. IMO a public blockchain is the way to go, perhaps with encrypted transactions, or perhaps using Zero Knowledge Proofs (ala Zcash) if privacy is important.  

To comment on your questions: 


Chaining blocks together provides a little more security as you could not just change one transaction in block X you would have to recalculate the hashes for each block forward and get others to agree to that change. In a DDB one could just delete/alter/change an entry.    
This would really depend on how the private blockchain is set up. Do we need others to accept each block? Would others recognize our new rebuilt blockchain? What consensus algo are we using here?
Blockchains offer a lot (in the right user case). In the case of banks transactions can be encrypted and only the parties involved have the keys to decrypt. Why have a blockchain to store competitors data? Well, what if the blockchain is used only for inter-bank transactions, and not for internal ones. Then there is a immutable (hopefully) record of transactions between banks.


Keep in mind that private blockchains are in their experimental stages. Banks like to make announcements for publicity, this does not mean that they have a working model or using the technology commercially. More often than not it is simply an intent to explore the possibilities that the technology can provide.