Eugene Volokh has been persuaded by Mark Kleiman that execution by torture cannot be reasonably provided by our legal system, but I never thought he was actually arguing that it could. Here's the bit of Kleiman's argument that Volokh found most convincing:
One reason is the tendency of power to corrupt, and for the conduct of the political game to become less rule-bound as the stakes increase. If the state has the power to torture, than the political process decides who is, and who is not, torturable. Those are high enough stakes to justify a considerable amount of cheating. (Would I help steal votes to prevent someone I cared about from being tortured? Of course I would. To keep him from being sent to prison, even unjustly? Probably not.)
A second reason is that putting torture on the agenda changes the job descriptions of public officials in a way that is likely to change the composition of the class of public officials. Presumably, if an execution requires a death warrant signed by the governor, a torture-execution will require no less. So anyone unwilling to sign such documents will be disqualified from seeking the governorship. You can think that there are arguments for cruel punishments and still be reluctant to be ruled by those most willing to order the infliction of such punishments.
That's a particular concern with respect to the office of juror. Under current American law, jurors who have scruples about capital punishment are excluded from juries in capital cases. Unsurprisingly, those are also the jurors most likely to vote to acquit. So someone accused of murder is more likely to be convicted if the case is a capital one. If the sentence were death by torment rather than simple execution, the exclusion of the scrupulous would leave a jury even more grossly stacked against the accused.
Those are certainly good arguments, but I didn't think Professor Volokh was claiming that his execution-by-torture preference could ever actually be implemented in law. Indeed, he ackowledged that his views are "pointless", "since they can't be implemented in my country without a constitutional amendment that isn't going to happen." And Kleiman's reasons are exactly why such an amendment would be impossible to pass. However, none of that speaks against the general principle of the justness of execution by torture in some set of very limited circumstances, and I'm not exactly sure what Professor Volokh has been persuaded of.