No PDA
William and Kate did not show PDA for a reason. They were, essentially, always at work. It is not a good idea to hold hands in the office, right? This was the same for them when there were cameras around, which was very often.
Official Photos
“The Duke and Duchess are almost always seen in photographs taken during official engagements, so they are at ‘work,’ and it would be unprofessional to hold hands,” explained HELLO! writer Emily Nash in 2017. She added, “They also need to shake hands with a huge number of people as they meet them, so aside from being on duty, it wouldn’t be very practical!”