It allows Google to access data that is denied to competitors. It’s a clear example of Google using its market power to suppress competition.
https://www.404media.co/google-is-the-only-search-engine-tha...
Whether by IP, user account, user agent, whatever
It may not be the kind of explicit anticompetitive behavior we normally see, but it needs to be regulated on the same grounds.
The website operator can do with that identity as they wish.
They could block it, accept it, accept it but only on Tuesday afternoon.
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"Anticompetitive" would be some action by Google to suppress competitors. Offering identification is not that.
The law may need more time to catch up, but search indexing will eventually be made a utility.
And that has an argument.
But in the general case no.