I'm sorry, but what part of the GDPR do you think demands invisibility? It doesn't even mention privacy because the GDPR stands of General Data PROTECTION Regulation.
The law does not mention privacy, correct, but its entire rationale is based on the idea of privacy rights.
The regulation isn't about fucking IP addresses, it's about big data collection information about, what you buy, where you go, who you are friends with and doing shady things with that data.
This can be achieved with more sane, pragmatic regulation.