What benefit was there in executing Anne Boleyn instead of poisoning her and pretending she was ill?

Question

When Henry VIII decided to abandon Anne Boleyn in favor of another woman, due in part to the lack of Anne Boleyn providing a male heir, he had her investigated for treason, adultery, and incest, and had her condemned, marriage annulled, and executed.

My question is simply, was there a political or legal benefit to Henry VIII in going through the charade of a trial and execution, instead of merely poisoning her such that she'd "fall ill" and die of "natural causes" in the eyes of the public?

Five months earlier, Henry VIII's first wife died, and had a blackened heart during embalming, leading to rumours of her being poisoned by Anne Boleyn. Perhaps the existing rumours of poisoning would make it suspicious of Anne Boleyn died of poisoning merely five months later? But then, why not use the existing public suspicions of poisoning of the first wife, and the public's dislike of Anne Boleyn, to instead put her on trial for poisoning the first wife, rather than the rather unbelievable crime of treason?

I just personally find the supposed excuses of her execution rather unbelievable, and thus poorly chosen, but perhaps they were believable enough to the public at the time?

All the claims in my post are from Wikipedia - I've added no interpretation or claims beyond the Wikipedia article of Anne Boleyn. My question has to do with possible political benefits of having a trial and execution for adultery and plots against the king's life vs other possible routes of disposing of his wife]

Answer 1

Since you're asking about potential benefits, and considering that this sort of debate could not be ending with primary sources, let's check the issue:

• Reasons for not putting on trial Anne Boleyn for poisoning: The king could not be the prey of gold-diggers: he should be able to control his marriage. So he would not be of political benefit to admit that he had his wife killed by someone he later spoused. On the other hand, rumors on that were of political benefit.
• Reasons for putting her on trial for adultery: Henry VIII had challenged papal authority with his marriages, but even for anglican, an accumulation of divorces offends morality. So the king should show that Anne Boleyn was a problem at the time he divorced from her.