I am sure that I am not the only one who feels this way, and I would hate to see SME project loosing many good testers because of this.
Yes, this is a problem, and that would indeed be sad. I am not aware of a way to hide the email addresses in the current version of Bugzilla. We are already seeing dramatically more follow-up to bugs in Bugzilla than we did in Mantis or at SourceForge, so in my opinion some pain is outweighed by the gain. We simply could not continue to use the SourceForge bug tracker for a project of this complexity.
We could change Bugzilla to require a login, which is a partial solution. However, that means that the current bug list cannot be searched.
Another partial solution is to do as I do - create a valid email alias just for Bugzilla work. The SME Server natively supports "extension addressing", so you can create your Bugzilla account as fredfrog-bugzilla@example.com (assuming you own example.com) and the Bugzilla mail will be delivered there. If the address gets harvested, you can change your Bugzilla email/account to something new and your bugs will follow you.
The best place to raise this is in the Bugzilla Bugzilla. And yes, you are not alone in your concerns:
http://www.redhat.com/archives/fedora-legacy-list/2004-October/msg00127.html