Basically it just happened that way. There were plans underway to crown Jane Seymour but they were postponed when plague broke out. She died before she could be crowned. I don't think Kathryn Howard was queen for all that long, so she wasn't crowned. And, I suspect, by the time Henry married Katherine Parr, it really just didn't matter all that much. The queen was still the queen, officially crowned or not. Also, coronations were very expensive and I suspect Henry balked at the expense for the last two.
I think Katherine Parr would have loved to have been crowned. She may have been lobbying for it behind the scenes, or perhaps the court party that formed around her was trying to push her coronation. She was a good queen in the traditional sense, and a good Regent when Henry was in France. She certainly would have felt she deserved it. Susan James points out that she kept commissioning portraits of herself, possibly as a reaction to Henry commissioning dynastic portraits with Jane Seymour enshrined in them, but also because she saw the regal value in them.Perhaps there were other reasons than the expense for her not being crowned. Possibly Henry had no expectation of children from her -- their intimate life is rather murky -- and felt that coronations should be reserved for wives who would be mothers of children, as having an anointed mother would be a political advantage for her offspring. (He was planning Jane's coronation but first her pregnancy and then her death intervened. Anne of Cleves he had no intention of keeping, much less breeding with. And he certainly was sexually enchanted with Catherine Howard and probably looked for her to have children; he was planning her coronation around the time of their trip to York, but possibly her failure to conceive changed his mind. She might have still been crowned, but then Cranmer ratted her out.)Also, there is another political angle -- an anointed Katherine Parr might have been in a strong position to claim the Regency after Henry's death. She certainly wanted to be Regent, and was disappointed when Henry's will turned Edward over to a special Council. If she had been crowned Queen, she might have been able to challenge this more effectively. Perhaps Hertford privately worked on Henry to prevent Katherine's crowning, or perhaps Henry himself simply didn't like the idea of her functioning in essence as Queen Regnant during Edward's minority.Perhaps there was a symbolic angle. The coronation ritual laid down that the Queen must be crowned with flowing hair, traditionally an attribute of a virgin or unmarried women; remember Catherine of Aragon went to her coronation with flowing hair, because Henry wanted to emphasize her virginity despite her widowhood. Katherine Parr was a widow twice over. I don't know how they handled it with Elizabeth Woodville, but perhaps the iconography would have been an issue for Henry.
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