Yes, it would be more challenging, and inconvenient, and probably a massive pain in the ass not to log IPs by default, but if the end result is a weakening of the power of modern social media companies (and political and law enforcement agencies) to exploit people's data for nefarious ends without consequence, then society as a whole, and the web, benefit.
Mind you, I don't necessarily believe GDPR is the solution, or that logging IPs is unreasonable, but I do welcome the conversation people seem to be having about who owns their identity.
If you're using a CMS then it's going to be type the username and hit "delete all comments"; maybe WordPress et al. do this already.
With a small blog the administration of that is going to be facile, surely.
And by the way, most blog comment systems don't require you to create an account before commenting. So this "have them post a comment using their credentials" wont work anyway.
Personally, I don't even think people should have the right to go back and delete a comment from years ago, which might have started a whole interesting discussion. But the EU requires that I think through such a system, including finding a way to identify them as the commenter and purge their PII from all logs/backups/caches as well.