Since you're asking about potentielpotential 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 poisonningpoisoning: 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.