I find the popular narrative people see in them intriguing. So many people are convinced, including on this thread, that the woman chased the prince. We even have this moniker, "Waity Katie".
Why? Because that's what wimmen do, but men are commitment phobic?
William has grown up knowing he's supposed to have children, and in the eye of the storm that resulted when his father put off getting married as long as possible and then married a fertile nineteen year old. He wasn't going to repeat that family mistake.
So he needed to meet someone roughly the same age as him from a family without many/any embarrassing relatives, and he needed to meet her early on, before she could acquire a romantic history of exes who would come out of the woodwork to sell nude shots to the Sun.
So, he went to university to meet someone like Catherine/Kate, who was intelligent enough to do A-levels and graduate university, but didn't have particular career ambitions. For example, a medical student would have been right out as a future queen, because she would not want to give up her plans to fit in with the royal family. Even William's own university subject seems calculated to maximise his opportunity to meet such a woman. You can bet your life that even if William had had a love of physics, he wouldn't have done it at university. Not only is it a subject with a high male to female student ratio, physics students tend to have more definite career plans.
And he met Catherine, and they spent years playing down their relationship so that she didn't have the maximum amount of tabloid attention and he waited until she was ready to get married and have the children.
And then they did that.