“she has no sense of justice”
People seem to develop a sense of justice through experience of injustice (either their own or others). There’s no evidence that Kate has experience of injustice. And therefore it is likely she has no sense of justice.
“she has no other personality, likes or interests”
I’m don’t think that’s fair. Kate is sporty, musical and likes fashion. And seems like a loving mother too.
But that’s describing most peoples’ interests and qualities. So it doesn’t make her stand out as being unique enough to be the only claimant for the crown of Queen consort.
“she is in it to the bitter end of getting the crown”
The crown may well end up being a bitter experience. The crown is a symbol of justice and that’s a heavy crown to wear even for people who do have a strong sense of justice.