Re: The problem here...
ICANN does not run the 13 root DNS servers. There are quite a few root servers operated by independent organizations.
The EU and the US basically agree on how the internet should governed. And that does not include governments having direct influence over the core aspects of the internet (IETF, DNS gTLDs, RIRs).
The problem is of course that the GDPR directly affects ICANN. But at the same time, the WHOIS service is not traditionally considered a core part of the internet.
So US government is in the tricky position that it doesn't like the effect of the GDPR on WHOIS and at the same time, interfering with the operation of the DNS gTLD would have massive world wide implications, which may cause damage way beyond losing WHOIS.