One of the key rights individuals have is to request that ALL PII about them is deleted from all of your records, and you have to comply with this request within a certain timeframe, and a maximum of 30 days. This includes backups, logs, everything.

Obviously, it's impractical to try to edit old backups to remove PII, so you have to be careful how you deal with logs in the first place - you might want them to be backed up on another machine with a maximum lifetime of a few days, you might want to not back them up at all and only backup your aggregated data, etc.

But keeping logs for a few days can be justified for as you saying DDOS mitigation, post-failure root-cause-analysis, etc, but the defaults for that data should be to delete that data as soon as it's no longer useful for that purpose, which for most companies will be a couple of days, maybe another couple for the weekend. You can keep it still further, for instance for active analysis, but the default should be to delete it as soon as possible.