Except like, not really? If you need to remove someone's data for GDPR reasons, then "if match == userId then delete" is pretty straightforward in your log aggregation store.
(Though perhaps one can meet compliance needs by keeping these logs only for a fixed maximum period of time, e.g. 30 days, and keeping only appropriately anonymized data longer.)
If your internal compliance people don't like it you can also rephrase it as "we are removing the data starting right now, the procedure takes 30 days". You have one month to even respond to removal requests, and can stretch that by another two. As long as you are not intentionally causing delays these are perfectly reasonable time frames.
Of course you still have to do all the other stuff for GDPR compliance, like making sure you have rules who gets access to the log system instead of just giving it to the entire company, making sure you store to an encrypted drive, etc.
Efficient or fast is not a requirement for GDPR, so it can happen slowly and in the background just fine.
In reality you need multiple different steps here: anonymous IDs, well-defined reasonable retention periods, strong access control and audit logging, and a privacy policy that says why the data is collected (for service quality typically) and how/when it will be deleted.
There's no one-clever-trick to GDPR, the law was intentionally designed to require businesses to apply holistic best practice. Whether it has done that well or not is another matter, but that was at least the aim.
GDPR request comes in, just delete the record the ID refers to and you're done.
First, as another reply above has mentioned, other data in the logs (such as IP address, list of friends, browser fingerprint) can be used to de-anonymize the pseudonymous ID.
Second, GDPR makes it quite clear (for the reasons above) that pseudonymized data, is still considered personal data. Pseudonymization reduces the risks, but does not remove them entirely. It should generally be combined with other measures such as encryption.