Only when several parties who don't trust each other need to write to a shared system, and none of them will accept an online trusted third party to arbitrate.

A blockchain is, at bottom, just a database with a very expensive extra property: it lets mutually mistrusting writers agree on a shared state without anyone being in charge. That property has real costs (throughput, latency, complexity), so it's only worth paying for when you genuinely can't fall back on something simpler:

• One writer → a normal database is better; there's nobody to distrust.
• Multiple writers who trust each other → a database with shared write access is enough.
• Multiple writers, no mutual trust, and an always-online trusted third party (TTP) they'll all accept → let the TTP run the database; still no blockchain needed.

The blockchain only earns its keep in the leftover case: multiple mutually distrusting writers, and no online TTP everyone agrees on. Everything else is a more expensive way to do what a database already does.

Go deeper:

• Wüst & Gervais, "Do you need a Blockchain?" (IACR ePrint 2017/375) — the primary paper this whole methodology comes from.
• Blockchain (Wikipedia) — background on the "shared append-only ledger" the decision hinges on.

A writer changes the stored state (in a blockchain, that's a consensus participant / validator); a reader only creates, reads, or audits transactions without extending the chain.

The methodology borrows plain database vocabulary and maps it onto blockchains:

The whole decision procedure turns on the writers — how many there are, whether they're known, and whether they're trusted. Readers barely affect the choice; they only decide public vs private at the very end. (Regulators and the people who maintain the blockchain software are considered out of scope.)

Go deeper:

• Consensus (computer science) (Wikipedia) — what a "writer"/validator actually does: agree on shared state despite faulty or hostile peers.