The main advantage of a blockchain is with the ledger price advertising between exchange members comes free.
I guess they can even implement OTC markets between peers, but I am not sure how do they plan to work with dark pools where parties want anonimity. Maybe they will just implement an internal blockchain with APIs for anonymous trading.
If you just used flat-file CSVs, and don't want to re-download the entire DB twice a day, you want to now come up with syncing strategies, merging strategies, and probably conflict resolution. If you just have a blockchain, then you get all of this for free (so long as your data fits the blockchain shape).
Though I imagine there's something else that can be used here as well...
Streams of messages don't work as well when you're multi-party, and the default state is offline, not online
Running transaction logs; you don't need to re download the entire DB twice a day. If you are disconnected, when you reconnect you give the last sequence number received. It is already built into FIX and other systems. Disconnects happen all the time in real trading systems and the ability to query past transactions doesn't go down.