How do we know they don't compete with each other? For instance, its been said several times over the years that Charles and Anne have a competition going between them about the numbers of engagements performed each year.
When I pushed for a documentation of back room work and meetings by the various royals in my post, it was with the knowledge that few members of the public look in the CC, either online or in The Times.
However, if there is criticism of any particular Royal for not performing enough engagements, a record in the way of notes, video, photographs etc of preparation for engagements could be used to reinforce in the public's mind, via the media, that in fact that Royal is working very hard. At the moment there is virtually nothing to document this extra labour. It all has to be taken on trust most of the time, and this is a sceptical age!