It's really pretty simple:
A law professor both having shown required competence and politicked enough to achieve his title, may argue that officers of the court in Nazi Germany were simply doing their jobs and following existing law.* However, if that professor is shown to have himself been an officer of the Nazi court, he may be put on trial or have the case examined by the bar, and being found guilty in either case, even if only of ethical violations, he may then be fired from his job. [Brian Leiter replies to a similar hypothetical here. One of my comments reproduced here] It's a bit formalistic but formalism is important: people in Cloudkookooland can say what they want, but if they come to earth and act on their beliefs they can be judged here, and then not be allowed back in.

Leiter is right but his contempt for the masses is annoying. Academic independence serves society by allowing people to think freely even when those thoughts are little more than dreams and fantasies. It's about the right of inquiry into unpleasant subjects, but also the right to risk sounding like an idiot, in both cases because in the long run the risks of error or absurdity are worth it.

"Academic freedom predates freedom of speech"
That's a good description but a lousy defense. The fact that that it wasn't obvious to Eric Rauchway is a problem.

The banality of self-importance. As I said in another comment on Rauchway's post, academic freedom predated free speech in the past for the same reason it’s predating free speech today in the PRC: it’s a both a pressure vent and a distraction, and technical advancement is important even in most authoritarian regimes. Academic free speech is an early example of the fight for broader rights. To acknowledge that the Crown saw fit to acquiesce is not a defense of the crown, nor is it a wise choice to use the crown as a defense of the prerogatives of academia. A historian shouldn't make such mistakes.

Also it's clear Henry Farrell understand's neither academic freedom nor tenure: "...an institution whose general merits I am somewhat ambiguous about ..." [#185 here]

I’ve suggested that academic freedom is a good thing on pragmatic grounds, but also made clear that it fundamentally depends on public willingness to delegate some degree of self-governance to the academy. If the public decides that academic freedom isn’t working out in terms of the goods it provides, then too bad for academic freedom.

If the public decides that democracy isn’t working out in terms of the goods it provides, then too bad for democracy.
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*The corollary to this is that if he'd made that argument earlier the odds are he wouldn't have gotten tenure. As Mark Graber pointed out there's a difference between legally arguable and morally correct. I was referring to the moral argument. Tenure and academic status generally are tied both to technically and socially acceptable practice.