When you don't trust the other people who may be writing to the data. The advantages of a blockchain are immutability and byzantine fault tolerance: regardless of how malicious your counterparties may be, they
can't rewrite the record of the state of the world, because every new record contains a cryptographic proof of the integrity of previous records. Also, this property is symmetric: there is no one person who is "hosting" the data and has full access to it by virtue of having physical possession of the bits. Even if you have physical possession of the bits of a blockchain, you can't rewrite them in any way that the other participants will accept.
Most real-world uses of blockchains (illegal dealings, adversarial relationship with the local nation-state, currency speculation & trading, gambling games) take advantage of this property. If you don't need it, you're almost always better off with an RDBMS, because you pay a heavy price in latency, transaction scalability, and data modeling for it.
Can't think of any business where you wouldn't trust your counterparties? That makes perfect sense, because people today generally do not do business with people they don't trust, because they can't. IMHO most usage of blockchains will happen in new markets doing new things that people would've considered foolhardy before, because its central value proposition enabling transactions that would've been considered foolhardy before.