There is no excuse for lacking an appeals system on site.
You realize that those who do need the most an appeal system are the banned users, those who can't access BB once banned ?
And (1) that isn't everyone who might use the appeals system, and (2) that is no excuse for lacking one onsite.
I can understand your frustration, but the thing is that for as infrequently as the appeals process is anticipated to be used, it would be inefficient to have multiple contact points to initiate an appeal, including increasing the opportunity for appeals to be missed. Furthermore, having the single point of contact be onsite would be impossible by definition for anyone who has been banned.
While I won't comment on your opinion that a non-email system would be better, as that's an opinion you're entitled to, I will remind you that the Terms of Service that govern all of our accounts does specify (section 4, Registration, last few sentences) :
"The registration form will ask you for other information about yourself ("Registration Data") which you represent and warrant is at all times true, accurate, current and complete, and which you agree to update in order to maintain as such. If you breach this representation, or Digital Field Theory has reasonable grounds to suspect that you have, Digital Field Theory has the right, upon notice, to suspend or terminate your account and this agreement and to refuse your current or future use of BuzzerBeater or any portion thereof. "
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The section on "Privacy" and the "General Provisions" section are also interesting reading, and if you're not comfortable with the idea of your email address being on file, i'd definitely suggest re-readng those.