It would be fair to your customers to have an on-site point of contact to initiate an appeal, and not particularly "inefficient" at all. What you call my opinion that a non-email system would be better is an interesting spin, one I don't see the point of. An on-site system would be fair, that is my point. I don't know why you call it a non-email system.
I do feel like I'm not responding to your actual concern, whatever it may be, because you've gone from calling the appeals process a sham to a phishing attempt to now something that is unfair because you can't do it directly onsite. I am only currently focusing on the 'not onsite' part because I don't see any reason whatsoever to engage you on the other parts.
On the fairness/unfairness of the actual mechanics of submitting an appeal: What is 'fair' is to have a formal avenue for appeals that anyone has the right to freely avail themselves of, regardless of their current status within the game. I am delighted that I am now a week away from celebrating ten years outside of the health insurance industry, but even a professional industry of that magnitude subject to ERISA and all the regulation on both the state and federal level still was quite within their rights to require that all formal appeals be submitted in writing to an address specified by them. It's a very specific, very formal process - you submit your case, you receive a notification that your appeal was received and then you receive a notification when a determination is made (plus any requests for information, etc).
When the point is made that there should be more notification given here, I wholeheartedly agree - and it appears that there is notification being given based on comments earlier in the thread, but I do think formalizing that would be an improvement. But the only way to respond to someone who no longer has access to the game is by communication outside of the BB site, and the only way for that person to initiate said appeal is also outside of the site. Requiring written notice of appeal to be physically delivered would undoubtedly be a ridiculous requirement, given the international scope of the community playing the game and the fact that it is entirely an internet-based game. Email is simply the standard administrative notification system above the game itself - you register for a team, you receive the email that it's ready. I presume the lost password/ password reset mechanism is also email based, but honestly I've never needed to test that. If you need to send legal notices regarding BB, those are also sent via email.
The short answer is that there will always need to be an offsite appeals process to handle appeals of bans from the game. Duplicating that process on site can open up the door to human error, so that for example a person who was banned from the forums and appealed in game might have his mitigation sent to his email address (since that's where game bans are necessarily sent to) and if the person doesn't check that email address routinely, would never know their appeal had actually prevailed.