Unless you're running child porn site I can't think of any reason to pay extra for a private domain registration.
I can give you some logical reasons why to pay for a private domain: If you change internet providers you would not have to notify past/present clients and/or prospects that you also now have a new email address. You won't lose out on communication you may not have been expecting. It also helps clients/prospects easily get to you, and it elevates your image of professionalism. Know what I think when I meet a professional who uses throwaway email addresses like [email protected] or [email protected], I think they are in it for the short haul or may intend to thow this address away and get another for some reason - they are called throw away email addresses and I have one for online purchases so I don't give out my business email address.
Oh, and by the way I'm an insurance agent, not into porn.