Michael Moore,
I think it's an interesting question.
One that has to be viewed in the context of the visual presented to the golfer as he addresses his approach shot as well as the visual presented by what he faces with the recovery.
The golfer's mind has adequate and immediate recall with respect to how he got to where he is, and as a result, there's an element of "why did I make that decision, or execute so poorly, combined with the prospect of the task that lies ahead.
All of these factors are related.
Now, the golfer must regroup, mentally and physically for the challenge that lies ahead.
Who isn't most proud of their miracle recovery from a dire location ?
It's one of the highlights of anyone's round.
And, who hasn't had their hopes and round dashed by a foolish mistake or poor execution, resulting in the need for a miraculous recovery.
So, yes, the recovery shot is certainly interesting and exciting.
As to fun, that's in the mind of the beholder.
I happen to like extracating myself from the jaws of doom.