And what would that do? You could say every murderer is mentally deranged so should no murderers go to prison?
No, you could not say every murderer is mentally deranged.
If you rob a liquor store and shoot the clerk so you can get all the cash out of the register, that doesn't make you insane. Just an asshole.
If you're fucked up enough to kill your own kids over the span of a decade, you probably aren't going to turn it around and become some exemplary citizen.
No, but maybe she can get treatment so she's not a big problem in prison.
Why wouldn't everyone who commits a crime just act insane and avoid jail?
It has very little chance of working.
If you're using the insanity defense, then you're already admitting you committed the crime. You have no option to say you didn't, or bring up reasonable doubt, or alternative suspects.
Second, you need experts to actually testify that you are insane. Believe it or not, doctors can tell when people are faking shit.
Finally, you need the jury to actually buy it. If you have zero history of mental illness and the state psychiatrist thinks you're sane, you're fucked.