A better example is probably
1. I general a keypair and commit it.
2. I send the public key to someone.
I *really* want to be sure that 1 is persisted. Because if they for example send me $1M worth of crypto it will really suck if I don't have the key anymore. There are definitely cases where it is critical to know that data has been persisted.
This is also assuming that what you are syncing to is more than one local disc, ideally you are running the fsync on multiple geographically distant discs. But there are also cryptography related applications where you must never reuse state otherwise very bad things happen. This can apply even for one local disc (like a laptop). In this case if you did something like 1. Encrypt some data. 2. Commit that this nonce, key, OTP, whatever has been used. 3. Send that datasome where. Then You want to be sure that either that data was comitted or the disc was permanently destroyed (or at least somehow wouldn't be used accidentally to be encrypt more data).