Exactly. Pedagogically, do you really want to be training students to send professional email (and they should make no mistake; e-mailing professors should be professional e-mail) from accounts named John_Stewart_is_my_bitch@Gmail.com? And already students are e-mailing professors without signing their names are identifying themselves. I suppose it just makes life easier for professors now -- if they don't recognize the name of the student they can just delete the e-mail. But how can you distinguish between spam and student e-mails at this point?

And the legal issue is huge. Most communication these days is via e-mail, and you should just never be sending confidential information to off-site addresses. Sure, you accept the reality that most students are probably forwarding, but you should be TEACHING THEM NOT TO.