It’s because she was in the public eye for a decade before she got married. So everyone thinks of her as Kate Middleton.
Added to that, there’s the issue “HRH Duchess of Cambridge” is a mouthful, and I think it feels archaic & overly deferential to some people to use these high-falutin titles in casual speech or ordinary prose.
Also, she is of the generation of women who commonly switch between married and own names, so it doesn’t seem a biggy to many of us. It upsets some people over 75, I think. The ones that address cards to “Mrs Robert Smith” or “Richard Jones Esq”.
So lots of reasons but generally we are a lot less formal and class-bound than we used to be.
Agree that “Duchess Kate” sounds bizarre to British ears, though. Like some Disney invention of what royalty might be. Which is odd because Princess Diana was commonly known as Princess Diana, which was just as wrong but somehow caught on. Maybe precisely because 1981 was that weird midway point between the starchy formality of the 50s (when the current Queen came to the throne) and the relatively relaxed attitudes now.
Which probably all sounds like madness but makes sense to my 70s born British perception of it all 