... which is crazy unrealistic, since it's "PII" that can only stay "private" by collective agreement of every node in the network, but no accounting for the reality of network architecture in passing law, I guess.

Maybe a deep expectation of anonymity while accessing a worldwide network of cooperative machines is something people should stop telling the public they should expect?

Under GDPR you can use all the PII you reasonably need to provide expected services, you don't even need separate consent. But, if you have PII, the moment you use it for other purposes, or obtain/retain/share without proper cause, you are breaking the law.

IMHO, that is very reasonable.

Real world example - giving your phone number and information to your car mechanic / doctor / bank teller / plumber is reasonable. Using that information to score girls or ask donation for a puppy shelter would be considered improper.

I totally agree, and I think the GDPR is also reasonable in that it allows you to use the IP address for essential security reasons, such as blocking bad actors based on IP address - it doesn't say "thou shalt not track IP addresses", it says you need consent if you're going to use it for anything that isn't essential for security or in your end user's best interest.

Or they can stay 'private' by not being stored or correlated with other user data. GDPR doesn't apply to the network itself, it applies to whoever is using it.

"Stored" is definitely the purpose of a router. "Correlated" can be necessary for debugging routing issues (or client-server connection issues that are tied to the intermediary fabric near the client doing something weird; hard to determine if an entire subnet is acting up if you aren't allowed to maintain state on errors correlated to IP address).

Where do you get the idea that GDPR doesn't allow you to process PII for the purpose of routing packets?