Of course, a modern reader has the benefit of hind-sight. We know that number three wife (Jane Seymour, who died in childbirth) is actually the exception to the rule. Yet, it should have been reasonably obvious by the time the king reached Katherine Howard (after Anne of Cleves, divorced, which debacle lost Cromwell his head) that it might not be the best idea in the world to have a pretty niece at court who might attract the king's interest.
Of course, there are some things people have no control over, and I'm willing to bet that when Katherine Howard caught the king's eye, her uncle (Earl of Norfolk) started practicing pre-execution speeches. (As a matter of fact, he survived her, but barely.) Nevertheless, at the same time, hanger-ons piled out of the woodwork, demanding kudos, rewards, estates, etc. etc. (it was the great age of patronage). And you'd think that a certain amount of uneasiness would have crept into the picture. That people would have, rather than running to attach themselves to this new, young and wholly reckless young woman, might have thought, "You know, I think I'll stay away from court for the next three years" (and probably some did).
Because it wasn't just Henry himself who encouraged the divorcing, beheading of his queens. Every queen was surrounded by supporters and detractors, and the detractors spent an enormous amount of time trying to figure out how to get the queen and her supporters locked up in the Tower. Kind of like if Kenneth Starr and the Clintons, instead of just holding legal proceedings and issuing press statements, had actually been trying to maneuver the other party in front of a firing squad.
But then, thinking of the Clintons and politicians in general, I decided that believing, "This time it will be different. This time, our queen won't do anything stupid to annoy the king" is what makes politicians tick. Otherwise, well, they wouldn't bother. But those who would willingly (and consistently) play such dangerous (and quite often, petty) games must believe at some basic level that they have got their finger on the pulse this time.
It makes me very grateful for us boring middleclass types who just go to work and pay our taxes. Idealists and politicians may get all the credit for making history interesting, but at least the middleclass survivalists keep history going.