So if Amazon sues Google, claiming that it is being disadvantaged in search rankings, a court should be able to force Google to log all search activity, even when users delete it?
Google can (and would) file to keep that data private and only the relevant parts would be publicly available.
A core aspect to civil lawsuits is everyone gets to see everyone else's data. It's that way to ensure everything is on the up and up.
Courts generally require far more data to be retained than shared, even if this ask is much more lopsided.
Which would be chump change[0] compared to the costs of an actual trial with multiple lawyers/law firms, expert witnesses and the infrastructure to support the legal team before, during and after trial.
Just erasing the userid isn’t enough to actually anonymize the data, and if you scrubbed location data and entities out of the logs you might have violated the court order.
Though it might be in our best interests as a society we should probably be honest about the risks of this tradeoff; anonymization isn’t some magic wand.
Courts have been dealing with discovery including secrets that litigants never want to go public for longer than AOL has existed.
Depending on the exact issues in the case, a court might allow that (more likely, it would allow only turning over anonymized data in discovery, if the issues were such that that there was no clear need for more) but generally the obligation to preserve evidence does not include the right to edit evidence or replace it with reduced-information substitutes.