No PDA
They chose not to show much PDA for a reason. After all, they are always at work! It is not proper to be touchy during work hours. This is why they refrain from doing so when there are cameras around.

No PDA
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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,” Emily Nash from HELLO! said in a 2017 interview. 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!”

Official Photos