Hello, I think you need to look at motive. And also to remember that this was a premeditated crime. (Also the Burke and Patsy theories are not medically sound. We know that JB was already dead when she received the head injury, which is why there was almost zero internal bleeding.)
So given that this was a premeditated crime, as a woman, I do not want to give John or John Andrew (at least one is a sexual abuser) a free pass, and blame Patsy or Burke. It's also worth nothing that if Patsy or Burke had accidentally killed JB (which is not medically sound), the family could have claimed that the little girl fell and hit her head.
It's important to remember that John and John Andrew WANT us to believe that Patsy and Burke committed the crime, which is has been not possible due to medical evidence.
So, since it was a premeditated crime, we must look at motive:
1) To silence JB so that she could not report PRIOR sexual abuse, including what may have occurred on December 23, 1996. (And fibers from John Andrew's EA device were found in JB's bed; not sure if they were also found in Burke's bed.) The police were called on December 23, 1996. However, the person who opened the door said that the police had been called by mistake.
JB was intelligent, articulate, and outspoken. Had she reported prior sexual abuse by John or John Andrew, she would be taken very seriously. Had Burke reported prior sexual abuse by John or John Andrew, he would not be taken as seriously. (I believe Burke was autistic.)
Therefore the MOTIVE to silence JB so that she could not report PRIOR sexual abuse is stronger than any MOTIVE to silence Burke.
2) To frame Patsy, or at least to discredit her. Obviously a judge or jury would not convict Patsy, but she was discredited and disgraced. People were willing to blame Patsy, claim that she killed JB by accident, and yet give John or John Andrew (at least one of whom is a sexual abuser) a free pass. Talk about sexism and bias.
There was an obvious MOTIVE to frame Patsy: ransom note included some of her expressions and choice of words. Also Patsy's notepad and writing pen were used. Patsy's paintbrush was actually used to strangle JB. (JB died from strangulation, and was already dead when she received the head injury). Now, if Patsy herself had strangled JB (and we know that she did not do this), she would have the intelligence to hide or throw out the paintbrush. (And would Patsy write a note to incriminate herself? She was an intelligent woman.)
Patsy's items that were used: paintbrush, notepad, writing pen. Plus the ransom note cast suspicion on Patsy.
What motive would John Andrew have to frame or at least cast suspicion on Patsy? He would want his father to reunite with his mother, NOT because he cared if his parents got back together, BUT due to John's WEALTH.
Therefore, John Andrew would have the above two motives. Remember that John Andrew's suitcase was found near JB's body. The suitcase contained a semen-encrusted blanket (semen belonged to John Andrew), a children's book called Dr. Seuss, and some other items. So, why was the suitcase near JB's body? Because someone (likely John the father) had every intention of disposing of JB's body, but also of disposing of the incriminating suitcase.
As previously mentioned, fibers from John Andrew's EA device were found on JB's bed.
Lastly, there has been some suspicion that JB told Melinda (her older half-sister) about the sexual abuse. However, I like to think that Melinda would have done the right thing, and reported this to police.
I believe that John Andrew also had a key to the house.
You need to also ask why John the father was not framed for the crime - only Patsy the mother!
And let's use common sense: a routine "sexual predator" would be more interested in framing the father than the mother!