Genuine question, do you have the numbers for other royal houses to compare? Because I've seen comment by a Dutch royal watcher on twitter moaning about William-Alexander going to another holiday of the year while doing less than the UK's lazy Will. (I honestly doesn't follow other European Royal families closely, so i don't know how "busy" they actually are)
Once I made comparison of the number and found that no member of Japan Imperial Family could even compete with William's number during normal year (back when William's number was 200-something. I don't have the number now, I lost it with everything else in my broken hard drive), nor any of them ever do multiple engagements in different sides of the country a la Anne. But then again, I only counted based on what's being reported since i didn't know how to find any info about closed door meeting similar to William's foundation meeting which was reported in the Court Circular.
During Workshy Will era, I remember reading an old article (I think it was The Sun) which mentioned that Charles (and Diana) doing moderate number of engagements (the article basically comparing him with his sister's and parents' higher numbers) and Charles's number only pick up significantly post-divorce (whether it was because his marriage or that his kids were both in boarding school). But back then, that article made me think that maybe it will be similar with William (that his number will increase after his kids are in boarding school, not that he would divorcing Catherine for his number to pick up). I'll link the article if google can find it, (or maybe
@Iluvbertie could kindly help with the tally

) so we can compare apple to apple of two Princes of Wales with young children instead of comparing them while in different stage of life.
I agree though about William's reluctance. He always gives me the impression that if he could, he would abandon his position, prefering living an aristocrat life than being royal (or even king) . He surely doesn't seem as eager (ambitious) of becoming monarch as Fumihito, the Crown Prince of Japan for example

. And with his comment about being royal with little 'r' instead of big 'R', I'm inclined to think that he plans to continue doing this way: big projects with less traditional public engagement (like the older generation royal have been doing) and more social media appearance (and I don't think recording social media message have ever counted as engagement). Would it be a correct move or not, time will tell.