GDPR blows up a lot of assumptions we make about writing software and managing servers.
Similarly credit agencies aren't required to comply with deletion requests either. You can't simply GDPR your way out of a bad credit score.
But it's a total mess, when you read the GDPR it's clear that it's written by people with limited understanding of IT. Of cause it has to be extremely strict, otherwise you'll end up with a Cookie-law 2.0. The cookie law from the EU was read by the industry in a way that clearly wasn't intended. It made zero different to user tracking, we just got a bunch of pop-ups stating that the site uses Cookie. If you read that law as I believe it was intended, the idea would be that you could say yes to cookies or no. If you choose no, the site would disable the use of tracking cookies. But was to much work, so people just slapped a cookie pop-up on their sites.
1) if you have a legitimate reason that allows you to process the data without consent (which would be the expected scenario; if not, then any sane organization would likely just choose to don't have that data in their logs at all), then none of the following applies, and you can refuse the request;
2) if you had a legitimate reason but "the personal data are no longer necessary", then you must comply.... but that's just duplication, you should not have had that data anymore since if you're compliant, you should have cleared the data out already. E.g. if you believe that you need (and are allowed) to store data for 6 months for purpose X; then you'd ignore the request for 5 month old data as you need it, and ignore the request for 7 month old data as you already purged it as a routine operation.
3) if you didn't have a legitimate reason and actually needed consent, then you follow the same process as you do for scrubbing references to all IP addresses which didn't give you consent. If you're compliant with the other requirements (which is tricky in this case), then the deletion request doesn't add anything meaningfully different.