Incidentally, many lawyers and law firms run their own mail servers for precisely this reason.

I think there's more to it than that. They want audit trails and backups, they don't want you reading email from unapproved devices, etc.

Yes, but it's a part. When I was a law student, confidentiality was named as the main reason why we weren't allowed to use Gmail for legal clinic work. If you just want audit trails and backups, there are other ways of accomplishing that don't involve outright banning use of a third party mail service.

"why we weren't allowed to use Gmail for legal clinic work."

Since that time (I assume this was a while ago, i can't imagine it was recent since most of these schools now use hosted email providers), almost every single state has issued opinions stating that storing email with a cloud provider does not break privilege.

AFAIK nobody has cared much since New York's ethics opinion in 2008.

Nope, this was still the rule for Berkeley as of 2012. Since then though, they've been replacing Berkeley's prior system with a Google apps. I'm not sure if that changed anything.

I should also note that there have been a couple of cases since 2008 where courts ruled that use of an employer's e-mail system broke privilege with respect to that employer. See, e.g., Holmes v. Petrovich, 191 Cal. App. 4th 1047 (Jan. 2011). It might be a stretch, but I could see someone trying to argue that Gmail use voided A/C privilege with respect to a lawsuit against Google.

There are also a lot of court cases the other way, and those cases were more about employment agreements, handbooks, and TOU, than they were about by general privilege breaking by using a cloud email provider.