Marital intimacy as we know it did not exist in Henry VIII's times. Marriages were arranged for political reasons - like when Henry VIII married his sister Mary to the aged Louis, who promptly died. Sometimes the couple developed a warm relationship, other times they didn't. In Henry's case he had his own chambers and attendants, his wives had theirs. While it's not PC in this day and age, the structure of society then required the wife to be subordinate to her husband. In judging Henry's actions and reactions it's important to use the culture of the time rather than our modern views, IMO.
The other factor is the position of the Queen Consort. If she conceives a child through an adulterous affair she potentially places a non royal on the thrown, hence adultery by a Queen Consort is treason punishable by death. Likewise her partner is supplanting royal blood. They are putting a cuckoo in the royal nest.
Indeed, even if she only behaves in a way that causes others to whisper she's had an affair she is creating future problems for her children. Remember Richard III and his brother George both claimed their brother Edward IV was the product of their mother's affair with an archer in attempts to seize his crown (Richard adding the claim that Edward IV's marriage was unlawful as well to usurp his nephew's crown.)
I would suggest that Henry's decision to have both Anne and Catherine Howard executed rather than simply sequestered away somewhere was consistent with someone who believed they had committed adultery. The law recognizes the defense of heat of passion to reduce murder to manslaughter because jealousy is such a powerful emotion. Henry's actions to me aren't unlike a man who learns his wife has cheated.
In retrospect many believe Anne was falsely accused - but given what Henry knew at the time (and remember there was no reason to disbelieve Lady Rochford at that point) and what he was told I think there's a strong case for believing he thought Anne and Catherine Howard committed adultery. In doing so they committed treason in his mind and the consequence under the law was death. To let either live would create problems with future offspring from a future wife.
I'm not defending Henry's actions, rather I'm trying to interpret them using the perspective of the time and culture he was a part of.
I agree with you but I don't think your analysis takes into account all the circumstances, including the real reason for Anne's downfall: she did not produce a son.
First, it wasn't an arranged marriage, there was intimacy between Henry and Anne. I'm not sure if it was love as much as lust and infatuation, but there was an emotional attachment.
Second, although I would agree that there was no reason for Henry to disbelieve the rumors of infidelity, there was no reason to believe them either. The charge of incest was, at best, flimsy. Mark Smeaton was around a lot and Anne openly flirted with Norris, but the cases against Brereton and Weston were incredibly weak. Their real crime was that they were Cromwell's enemies. If Anne had borne a son, Henry not only wouldn't have believed the rumors, he would have taken severe action against anyone spreading them.
Once Henry decided to end the marriage, he couldn't let her go to a nunnery because that would have raised questions about the legitimacy of any male heirs he would have had.
It's interesting to contrast Anne with Catherine Howard. I think Catherine Howard was guilty, but would it have gone differently for her had Henry still hoped that she would bear a son? Henry had a healthy heir and didn't have anyone waiting in the wings, but he was growing impatient with her (?) lack of fertility.
I'm also fascinated by the differences in how they were treated after they were arrested. Anne had been anointed queen. She was taken to the Tower of London and had several ladies in waiting. Catherine was kept in Syon Abbey and, IIRC, had only one lady in waiting (I'm not sure who attended her after Lady Rochford went insane). Anne had a trial, while parliament issued a bill of attainder in Catherine's case. Anne was dead within 3 weeks, while Catherine languished for 3 months, even though Catherine was stripped of her title within a couple of weeks of her arrest. Henry annulled his marriage to Anne but, according to Allison Weir, didn't annul his marriage to Catherine.
Of course, a major reason that Anne was dealt with so quickly was because Henry wanted to marry Jane Seymour. But I'm not sure why wasn't Catherine Howard wasn't executed sooner. It's hard to believe that Henry seriously considered allowing her to go to a nunnery but, based on the delay in her execution, he apparently was reluctant to have her put to death.