I think the point was to Be Seen, and that everyone could then get a good look at them being greeted and then entering the church with their cousins. Now, if I was on somewhat shaky ground with the senior royals I wouldn't try kicking the hornet's nest. A discreet side entrance could have put them face-to-face with Charles before he took his seat. Not sure about that, but if the object was to Be Seen they could have exited with the family and caused a bigger impact from the surprise of it.

We'll see how taking Andrew's advice works out for them.

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