That's exactly why GDPR is a good thing. It prevents anybody from doing statistics and keeping analytics about the users. Want to collect this information in order to profile your users and offer them a better product (ndr. better ads)? Well tough luck. You either anonymize and stop profiling and tracking your users or you close shop in Europe. I don't see how this is a bad thing in any possible way. You say it costs money? I guess then some of the money they made by targeting users and selling their personal data so far can be put to good use.
If the user gives you their email address to register, you can ask them for consent to store it. In fact, most European websites that collect any kind of personal data have already been doing this for over a decade.
If the information can be used to build a profile linked to me, it's PII. If you do not and cannot link it to me, then it's no longer PII. That is kinda in the name, Personally Identifiable Information. In short, if the collection of information can point to me, it's PII. If it cannot point to me it's not PII.
Problem is, if we take it to extreme, we are basically playing Cluedo game.
Is "18 year old" PII? - no
Is "orders pizza every Friday" PII? - no
Is "always misspells word cheese" PII? - no
Is "leaves 10% tip" PII? - no
Combine it and you have PII.
And rightfully so. If the collection points to me, then it's PII. Anonymized it might be "is between 18-25 years old", "orders fast food once a week", "tips between 0-10%".
Just because something it murky, doesn't mean businesses get to ignore it. The entire point is to force companies to actually think about what their data is and decide if they need to store PII. If they do it have implications. Have a reasonable explanation for choices, and are willing to rectify issues pointed out by consumers and/or DPA.
If it is for fraud-prevention, then that is sufficient reason to keep it unanonymised...