You can build a Merkle tree from any data that is append-only; Git does this, as do ZFS and Dat/Hypercore. That lets you make strong assertions about data integrity, even without blocking local writes.
Now add a mirror: git upstream, FS snapshot, immudb replica, etc…or even just an outside log of the merkle proofs themselves. Then, if your database ever fails a check against that proof, you know the data has been modified, not just appended to.
To use a familiar Git workflow example: you can do whatever local writes you want, but if you disallow force pushes no one can erase history on the upstream repo.
Put another way: if you have immutable backups you don’t need a blockchain to ensure data integrity. OTOH, if you can’t trust your own infrastructure even as far as a secure remote backup you have other problems that a blockchain won’t solve either.