What is your feeling in front of an awe-inspiring photograph (with really good composition, light, color, depth of field, etc.) but with unsatisfactory technical qualities (for example: JPEG artefacts, lack of sharpness, banding, noise, etc.)?
It's all about the reaction.
Nothing else matters.
Every photo tells a story. The story is more important than the technical quality of the photo. If the story is strong enough to move people, the photo is a keeper, regardless of its technical imperfections.
And a technically perfect photo can be comletely devoid of any emotion.
A powerfully evocative, techincally perfect photo, is when you have captured magic.
By definition, an awe-inspiring image makes me feel awed. If I felt something else, it would be that else-inspiring.
If the quality issue is not part of artistic expression, the image just has to be that much stronger to evoke the feeling.
For my 30th birthday, my father gave me a photo of us together when he was the same age. It was an awesome gift. Was it ruined by the photographer's shadow? Nah, I never noticed it until several days later.
I'm going to tackle this from a different art, because I think it's not a question that only lives in the world of Photography...
What is technically perfect? I'm a huge fan of the band Rush, one that is often seen as a technically perfect rock band and yet they have never managed to hit that critical mass that sends them to international super-stardom. They have a huge following, around the world, but they polarize people with love or hate. So, one could argue that they do not inspire awe, at least not enough to live amongst the giants.
On the other hand, a band like the Beatles was not technically perfect. They were very, very, good, but I can find better drummers (my first paragraph contains a prime example!), better guitarists (can you say Clapton?), and so on. What did they have though? They had the art of music sewn up like nobody else. They could just take you places that nobody else could and it wasn't because of how well they played their instruments, but because of how they put ideas and concepts together. That makes them timeless, despite the fact that there has been better at the technical aspects of music since.
The message there, I suppose, is that artistic, awe inspiring, images are what they are. You will, I think, know them when you see them and the technical aspects of them will really be meaningless.
Some recent news photos are coming from cell phone cameras. If they tell a compelling story or bring something important to light (no pun intended), then they're "good" or even "excellent" even though their technical quality may be quite questionable.
I had a very similar conversation with another photographer along these lines:
"X, y, z is wrong in that photo"
"Right, but they don't effect it, and ignoring the rule of thirds worked better"
"You need to follow these things, if you had it'd be better"
"Okay, fair enough, but y is wrong because I purposely wanted to get it"
"Yeah but if you'd done that you'd get a more perfect picture and if you'd changed your aperture to x..."
The technical aspects of photography are great, and the science behind it is fantastic, but anyone who says that you've created an image that's technically not perfect forgets one of the biggest aspects of the art. That it's an art.
There's fantastically technical photographers out there but the images are often soulless and leave me cold, I respect the level of skill but there's nothing exciting. Some of my favourite photographs are almost technically perfect, but the imperfection makes it feel more real, more human.
If you see a photograph and you like it and you keep looking into it, there's something that has grabbed you attention and is keeping you fixed to it.
In simple words, if you like something you see at first glance, it's good.