From AI:

"Not guilty by reason of insanity" (NGRI) is a legal defense that a criminal defendant can use when they admit to committing a crime but claim they were mentally incapacitated at the time. The defense is based on the idea that people who are not acting as free moral agents should not be punished.

To use the NGRI defense, the defendant must prove that they were legally insane at the time of the crime. This means that they were unable to understand the nature of their actions, distinguish right from wrong, or resist the impulse to commit the crime. The defendant has the burden of proving insanity, which is different from the "beyond a reasonable doubt" standard used in other criminal cases.

If the defendant is found to be insane, they will not be incarcerated in prison, but will instead be placed in a mental health facility until doctors determine they are sane again. They will not have a criminal conviction for the offense.

The NGRI defense is difficult to prove because it requires meeting many conditions. Various jurisdictions use different tests to judge insanity pleas, such as the cognitive test, irresistible impulse test, or substantial capacity test.

No lawyer here but I’m fairly certain you’re wrong about that. Innocent by reason of insanity is something I recall seeing.