There's that. Also your affiliation with the client may (read: will probably) show up when someone pulls a credit report. IMO, my employer, landlord, bank, et al do not need to know with whom I do business.
Another fun aspect of GoDaddy is that GoDaddy will fine you if someone complains about your fake/inaccurate whois info.
My current registrar is Gandi.net and they have been great; whois privacy is included wrt this thread. I left GoDaddy in a SOPA-induced rage and haven't looked back. Of particular endearment to me was Gandi's No BS policy: https://www.gandi.net/no-bullshit