I think Djokovic is indeed an extreme example, but the trend isn't uncommon for players of this quality. They can play incredible tennis, but it requires an extraordinary amount of concentration and focus. To do this for a whole match is very difficult, arguably impossible (when talking about long matches). That Djokovic has a very strong control over WHEN that focus is at its height, is a quite important characteristic that makes him such a great player. All great players have a degree of control over this, but some to greater or lesser extents. For those people who play tennis, they will recognise what a rare skill this is. Simply trying to focus harder is not sufficient, it is a genuine skill to be able to 'tune in' the way that these top guys can when they have to. When Djokovic is feeling good about his game, it feels like, should he want to, he can pretty much make himself a wall, such that only very extraordinary tennis from an opponent can win them the point. Djokovic enjoys having a rhythm, which may go part of the way to explaining why he can only seem to bring that level a fair way into a match. Add to that how much adrenaline helps and it paints a fuller picture. Djokovic also has an advantage in his playing style, which is that he returns so very well. What this means, is when he reaches that level, it is less frequently hidden by failure to impact on serve. For comparison, Federer can tune in with an opponent serving at *5-4 (ie, needing to break) but be less likely to take advantage of that focus because his return game is more passive than Djokovic's, the same is true for Nadal.
Edit: this is all off the top of my head so may be messy and probably requires more thought.
I agree that it's a greatly important specific skill and about the "becomes a wall" thing, but I can't think of many players like that, Hewitt yes, as Statracket mentioned, but I can't think of many others.
Besides, being able to focus constantly for a match doesn't look that much like a rarity to me in top-tennis. Nadal may be the best at that, maybe, but many other players enter that scheme imo (as he has been mentioned, imo Fed is less constant than Nadal but he's more in that scheme imo). You may be right about the "management of a long match" thing, but Djokovic's problem doesn't only appear in long matches imo.
And it would surely be easier for Djokovic ... and his fans
if he was able to play that level all match long.
Is it impossible for him ? maybe not (not sure : in a few matches he could play that level from the start to the end), Statracket and you may be right, but then it's both a quality and a problem imo.
I also think like Statracket that it may mean that his game needs adrenaline to be at his best, as it was also the case for Hewitt. And that adrenaline level is imo what separates him most from Murray for instance, even though it's not the only thing.
The fact that Djokovic needs rhythm is another explanation you bring here and which sounds accurate to me.