One way to do this is with S3, for example, is to use an IAM role with only the "PutObject" permission, and enable object versioning for the bucket to prevent a compromised server from being able to delete data by overwriting existing files.
Maybe the extra layer doesn't add much security, but if it's a simple config change and it does add something, wouldn't it be worth doing?
You could make a similar point about the centralized backup management server - it needs to have "some kind of login" to all your production database server, so of that host is compromised (which might only store encrypted copies of your backup), so are all your database servers if those privileges can be escalated. You could argue that one backup host is easier to secure than a complex system such as AWS, but then I would argue that it would probably be hard to beat the track record of S3/IAM. ;-)
Both approaches have their place. If you're dealing with a large number of hosts and a lot of data, the backup host will quickly become a bottleneck and you're probably better off with the append-only approach. If that's not a concern for you (i.e. you're not running into any bandwidth limits on the backup hosts) and want to deal with operating yet another service to avoid the risk of e.g. IAM privilege escalation, the other solution might be a better fit.