I'm also tired of some people saying that anyone has to "prove" their worth. First of all, worthiness is every living thing's birthright (humans, animals, plants). You don't earn worthiness. You are born worthy.
You earn respect. You earn admiration. But you are born worthy and (if you are lucky) you are born loved (tragically, there are many people who are born without anyone to love them, even though they deserve it by right!)
Sure, we all have more respect and admiration for hard-working people who work from the bottom up, etc. than we have for the young "aristo-brats" who go to the fanciest schools but then do nothing with their lives except party, snort cocaine, and shop. We look at this stereotypical sort of "aristo-brat" and think, How do they justify their existence? But we forget that it's all internal. Usually, the "aristo-brat" is actually a very worthy, loveable person, but his/her talents and potential have not been tapped and it usually takes "inheritors" longer to mature than "ordinary/average" folk.
Kate is the daughter of two over-achieving people, self-made millionaire business partners. She might have insecurity about that. How does she rate, how does she measure up? She goes to Marlborough College, to St. Andrew's University to study art history (a very "aristo-brat" type of degree) and she leaves to join the Sloaney set in London. We see her shop, go to William's polo matches and the occasional "it" party.
She just needs to find herself. Somewhere under all that exterior crap (the tabloid stories, the "socialite" lifestyle) is a very special human being who well might be hiding a reserve of gem qualities.