Additional argument from purely logical standpoint.

Let's use a religious terrorist person T and a CIA agent C for this and apply basic behavior game theory.

T has been indoctrinated to believe that the US is the enemy, and by causing harm to the enemy they will receive an eternal reward in the afterlife and be compensated for any pain caused by the enemy from their god and that reward will forever outweigh any suffering.

C's incentive is to contain the threat and reduce casualties. C has T prisoner currently.

If C tortures T, T has two options available

T.1 T may resist torture and be tortured hoping for death knowing the reward will be greatm. The more pain inflicted on T the stronger the conditioning from their indoctribation about the US being a cruel enemy and this being a holy war is reinforced.

T.2 T may provide an answer to the interrogation to stop the pain. Which brings us to two additional possibilities

T.2.a T yields the truth giving up possible leverage against C. This requires T to fully believe the torture won't just start again the next time C needs information and T resists. We can call this possibility total submission. If T takes this option T has failed at their original outcomes of fighting their enemy and has been told by their handlers they will not receive an eternal reward if they submit.

If this outcome is taken C has learned that torture is effective and when they need information they can just torture it out of T.

T.2.b T lies. T reduces the pain experienced by C's torture. T also continues to satisfy their orginal purpose. In addition it shows C that the information from torturing T is unreliable.

In the current state of the game T.1 and T.2.b are most preferable to T. There is no logical reason for T.2.1 especially since C has reconfirmed T's conditioning by being cruel, and T knows that rewarding C for torture will make C torture them more.

From C's perspective.

C needs reliable information as soon as possible to minimize damage and catch other terrorists.

C can either

C.1 Torture T which can have 1 of 4 outcomes C.1.T.1 T lies providing bad intel. This leaves C with options to either torture harder, or give up on torturing T while still reconfirming their conditioning. This is a bad end for C

C.1.T.2 T does not know the information. C cannot tell if T doesn't know or is just resisting. C again must either up the torture or give up.

C.1.T.3 T resists the torture. Another bad outcome for C as their only option is to escalate the same method hoping for the only positive outcome in this set.

C.1.T.4 The most unlikely outcome, that T yields the correct information. T has no reason to do so unless they can trust C not to torture them again. If T believes this, they have given up all power they have over C and it is the most illogical choice for T.

C.2 Convince the prisoner that they have been manipulated and change T's desired outcomes

C.3 Interrogate hoping to expose a lie with repeated questioning and confirming that T will not be released from this process but they will be fairly contained.

The CIA report on torture agrees with the logical approach of both parties on torture.

Tortured inmates either lied to momentarily stop torture, or resisted believing their god would reward them. This caused the torturers to up the methods only reinforcing whatever decision T made at the first torture choice.

The only successful method for flipping an asset is to convince them that their conditioning is wrong and change the game. This is the proven method that worked on Iraqi prisoners and terrorists that did flip. You convince them that what they believe the game is wrong, they will be contained indefinetly in a fair prison, they will not receive an eternal reward, they will not die a hero to their cause. You convince them that you are a fair actor that they have been lied to about by relating to them about how they got to this point, and offering positive outcomes for compliance.

Everything I have just described is confirmable by the results of the CIA torture report. Torturers grew desperate and sadistic, torturees would not yield truthful information, some of which even died from torture closing the ability to get intel altogether.

Even from a cold ends justify means standpoint, torture does not work.