One of the few practical uses of WHOIS data is basically so ICANN have an address on file for when someone wants to dispute your ownership of a domain on trademark grounds. Anyone who registers a gTLD is forced to submit to their private dispute resolution process (UDRP) as part of their agreement with their registrar. There’s literally no way to opt out unless you don’t want a gTLD, thanks to ICANN’s total control.
There's also (very bad) precedent in the UDRP for using out of date or inaccurate WHOIS information as evidence of Registration/Use in bad faith. There's even been cases where a UDRP panelist has argued using WHOIS privacy services was prima facie evidence of bad faith, which beggars belief.
http://www.udrpsearch.com/naf/1684372
"This Panel member is persuaded there is bad faith registration and use because of several factors. The first factor is using a privacy service in a commercial context raises a rebuttable presumption of bad faith. Respondent has done nothing to rebut that presumption. Respondent does not need to conceal its identity from the marketplace to be a domain name reseller. Respondent offers no explanation as to why Respondent concealed its identity (and conceals it to this very day). Only people with an intent to deceive conceal their identity, which is the very definition of bad faith. Since Respondent did this at the time of registration and through the present day, there was bad faith registration and use of the domain name."
Thankfully other panel members dissented, but the UDRP has a long history of questionable reasoning and decision making, and bizarre WHOIS issues are not unheard of.