Identity. Once you log into a website a MetaMask address, a lot of things begin to come into focus. Create as many as you want, move contents around, etc. It's a lot more empowered than google/fb oauth feudalism.
Physical and intellectual property registries. Could be far more efficient, accurate, and resilient to bad actors.
If you only need an informational registry for well-behaved cooperating parties, you don't need it to be completely trustless. There are many other ways to decentralize storage and ensure consensus when you don't require mexican-standoff level of distrust.
Specifically, the thing that is essential for most property registries is recognition and enforcement by a meat-space government. So, while a digital ledger is a good idea compared to, well, lots of existing property registries, decentralization/trustlessness isn’t important, adoption by a trustworthy and capable enforcer is.
How will blockchain make it better? Unless you've figured out how to have a computer figure out what inventions should qualify for protection and what infringes on them, I don't see it.
You're focusing on patents. Countries operate copyright offices--clerks, submission fees, red tape, human error. With blockchain, I can produce and store an md5 of a audio file, pdf, or video for next to nothing. You now have cryptographic signed proof of generation at a particular time, and a system that stores the data perpetually. Yes, you still need courts and judges to adjudicate conflicts, I never said it was a 100% solution.