A coming of age story doesn't necessarily mean "getting old", I think. Up is not really a coming of age story but it's an interesting case to look at. It is true that the first ~15 minutes of Up is super sad and compelling, but I think the hundred minutes that follows it is more of a coming-of-age story. There is a clear character growth in Carl during those hundred+ minutes. It's more of a coming of age story because he learns how to be happy with his life and to care for others again etc., while before he had an almost childish obsession on completing his dream on his own. The point of the genre I think is to condense character growth into a shorter (chronologically speaking) story. That's why a child or a teenager is often used, since they usually start with little experience and go through change very quickly. If the story is 4-year long with time skips, we'll end up with another Grim Fandango (not that I'd be complaining.)
This is a good point to bring up, though. It's not really necessary to have young children as protagonists. We don't really know where that idea is going yet, though. The children might become a metaphor for Tim's experience in the game industry, or for adventure games themselves. I'm really interested in seeing where it goes.