That's what the full-time solicitor at my company said. It will be like PPI, only worse.
The big punitive fines people are talking about are the ones available to the regulators via a separate mechanism. As far as I can see, they do potentially apply to technical breaches as well, but that's quite a different context legally speaking.
You don't have to purge your system of all PII upon request. An IP address is only considered PII if it can be used with other data to identify a person. If you delete the user's account, you can keep your server logs with IP addresses as long as you have a compelling business reason.
That reason is "security and monitoring".
Really most of the GDPR is just best practices codified. You are only really in trouble if you are using customer data for purposes that you A) haven't received their consent for and B) aren't what the customer would expect given what they are using your service for.
If you are able to map the IP to a user then it becomes personally identifiable but the IP itself is not.
"a. the personal data are no longer necessary in relation to the purposes for which they were collected or otherwise processed;"
Because the data is still necessary, you don't have to delete it.