Cryptography based Banking
There are lots of good reasons to not base money transfers on arbitrary numbers that you need to keep track of. Right now, banks have to make sure themselves that a transaction is legitimate and may never lose record of it, otherwise money just disappears to someone's damage. With a blockchain, you get a hard proof a transaction took place. Whether that's to proof you paid for something or for law enforcement to know you bribed a certain someone, I firmly believe it's better than what we do now. If my bank told me tomorrow I have no money or claimed I spend it all on terrorism, I would be in a pretty bad spot.
Ownership and Track Records
We live in a time of misinformation and AI generated bs. With the help of a blockchain, you can keep track of who posted something first, i.e who has the copyright or started some false information campaign, and also who generally spreads bs. This of course also works the other way around: Who has a good track record and posts trustworthy news or original content? And again, you wouldn't necessarily have to rely on a single institution to play nice, not delete content etc. Although admittedly, it's much more complicated this case, because you have to expect bad actors much more than in banking. Banking is infrastructure, this can be a lot of things (science and/or opinion and/or legal stuff...).