To play devils advocate
Getting a warrant requires establishing cause. Using public information can certainly help with that. If you have location data that places someone at the scene of a crime, that is going to help you establish cause and convince a judge to grant you a more intrusive search of your person/effects/property
Even if we take for granted that privacy is right, is worth having, should be respected etc, what is the benifit to society in denying law enforcement the ability to do anything Google, Walmart, or the creepy guy down the street willing to pay a few bucks for PI certificate and a few subscriptions can do?
The real question I think we should be asking is not how mad we are about government purchasing something for sale, but if it should be lawful to produce and sell that stuff in the first place.
Now I don't think GDPR is a very good model because I don't see a lot evidence of its efficacy. It looks like a lot of really costly window dressing that mega corps spend a lot of money maliciously complying with, while disadvantaging everyone smaller in the market place. However it probably is a rich source of lessons learned as far as crafting better legislation.
The real issue if you ask me is anonymized data, that isn't. Especially in the era of fast cheap ML we are now entering. I have seen far to many data sets out there where people say stuff like "legal says its only got one indirect identifier so it isn't PII" but with even the slightest bit of imagination and correlation with a few other public data sources, you can easily get back to individuals with a high record completion and degree of certainty/accuracy. Of course if we tighten the definition of what you must consider "Personal Data" that creates a lot of security problems if say 'a high resolution time-stamp' might count, and obviously it will make doing all kinds of legitimate research much harder as well.