I can't imagine that most would not pick the dog work answer....kind of expected on these boards.
Especially if the word "important" is asked.
The shot is simply a portion of the entire event and any importance to me relates most to a second by second measurement and encompassing all involved.
Importance continually shifts, in other words.
So, while I would not shoot a self-flushed woodcock for obvious reasons, I see little reason to not shoot a self-flushed pheasant any time(providing a nearby dog has not misstepped and a shot would be an incorrect reward of sorts)...or a ruffed grouse when they are found under most conditions present today.
I don't find that relates at all to any lowered personal opinion of or giving less value toward any dog's work so implicit in the question.
Limiting shots to points only is more a way of lessening hunter impact on a strained bird population than indicating importance, to me.
And were I to shoot only a bird my dog pointed then my friends dogs may well feel slighted.
In fact, a friend's dog pointed a ruffed grouse a few days ago in the U.P. and I had no shot at the flush. The look Amber gave me was priceless...so, I reckon if a friend's dog points or a rooster jukes the wrong way and arises cackling, I'll shoot at it.
It is a plan that has worked reasonably well for many years.