It should be noted that Brave is not an advocacy group; they're a medium size for-profit company, with a business model that stands to gain if Google is cut down to size. So even if their complaint seems valid, calling on regulators to shut down your business rivals is shady, and you should take any representations they make with a pile of salt.
I also maintain my general skepticism that Google's business model is illegal under the GDPR. If the regulators had intended to make Google illegal, I'd think they would have said that.
First, they're not calling on regulators to shut down Google, but to make sure they respect the GDPR (and thus their users' privacy). Second, the regulators didn't intend to make Google illegal, they intended to establish respect and moderation in the processing of users' data. Of course, it's obvious for everyone that the companies doing the massive data gathering are mostly American (Google, Facebook etc.) and that European competitors to these giants could potentially profit from this, but that's just a (very welcome) side-effect...
It seems very clear to me from the content and tone of their article that their goal is to get regulators to hurt Google. There's a lot of discussion about how dastardly Google's being, and of how different their business will have to be after the enforcement action, but very little about which specific wrong things Google is doing.
Google should not fear audit of their internal data handling practices, and the way it communicates with data subjects about the purposes of data processing.
They would say something along the lines of "I gave Google my data for purpose X, but they're using it for Y and/or claiming the right to use it for Z, what's up with that?".
They would not have a "Purported Legal Basis: Unknown" column with a scary red background in their spreadsheet.
If you actually believe that your competitor is evil, and their business is built on unethical behavior, then getting regulators to do something about it is a reasonable action even if it does benefit you as a company.
Yes. Constant legal sniping is endemic in some industries, but it's pretty rare in tech. As far as I know, Google itself has never demanded that its competitors should be fined.
Most of them? There's a world of difference between "we're competitors", or even "we think we're better"/"we deserve to win" vs "our competitors are Bad and should be the target of legal action".
I also maintain my general skepticism that Google's business model is illegal under the GDPR. If the regulators had intended to make Google illegal, I'd think they would have said that.