Backups do not solve the problem of not knowing whether data you just wrote to disk will still be there in the event of a power outage or system crash. You know, before a backup has a chance to run. Sure, those events should be extremely rare but that doesn't mean that we can or should just ignore it, at a large enough scale even extremely improbable events are guaranteed to happen.
Backups do not solve the problem of not knowing whether data you just wrote to disk will still be there in the event of a power outage or system crash.
It's not a "problem", it's just reality. You can't predict when exactly the crash will occur relative to the disk write or backups.
The OP has nothing to do with backups. fsync(2) and friends are also necessary to ensure correct ordering of writes to disk, which in some ways is more important than ensuring that the data is actually committed. If certain writes aren't written in the order expected, then applications lose crash consistency and now you have corrupt data, not just missing data.
In many applications, crashes are less of a problem than falsely believing a write happened persistently. Consider a mail server: if it can wait until the message is really saved before returning the final success response, then a crash means a retry later (and maybe a duplicated message if the crash happened in the small window between the write committing and the response going out) rather than a lost message.
