This is just my observation, but it seems like Standard American English lacks any distinct accent when speaking. Listen to almost any person singing with an accent, and they sound like any American singing! I suppose this could be because America has had so many accents thrown on to it that it's averaged out, perhaps. Is there any explanation for this?
I suspect you're coming in from a false assumption. Accents are a combination of many factors, the most notable being vowel pronunciation but also including stress patterns, intonation, etc. However, in common usage "accent" also means dialect or vernacular which would include slang and colloquialisms, tag questions (as a Canadian, Americans often tell me that they love how my "accent" means I say "eh?" a lot), etc.
Pretty much all of those disappear when singing. They're overwritten by the melody and time signature of the music. Slang and colloquialisms are less prevalent in music (especially pop music which sells to an international audience). As for vowel pronunciation, it's not uncommon to mangle pronunciation in service of the rhyming scheme.
So what I am saying is that one could argue that when singing people have neutral accent allowing listeners to fill in the blanks with the accent they are most familiar with (their own).
For an example of this, listen to pretty much any song by Adele (who is from Britain). Personally, while she's singing I'd agree that she sounds "American" (actually, I'm not American so I wouldn't say that. I'd actually say "she sounds like me") but if you actually listen, her vowels are very British.
I found a source to back up my reasoning but it's hardly a peer reviewed academic paper.
British popular singers do tend to sound American -- but obviously not the choristers at King's College!
I wonder if Americans can spot the difference though? Does it make you cringe -- like actors doing bad accents? It would be interesting to hear how Americans feel about this. There are so many US accents, as well as Canadian, perhaps you just don't notice.
As an amateur singer, I try not to sound as if I'm deliberately faking a US accent, but it's difficult -- especially when a song is 'Southern'.
Listen to these recordings. I don't think they'll all sound the same to you.
You can group accents into larger groups according to shared features. But it's certainly not the case that they all sound the same. If you want to look for accents that are very different from the standard, look for areas where diglossia and language contact more in general play an important role.
If you are referring to public speakers in particular, I suspect the fact that they have very similar accents can be accounted for socioliguistically: most of them are trained to speak/sing in the most standard way in order to be easily understandable to wider audiences and recognizable as part of the system they represent.
I think the academic phonological analysis is true only to a small extent. It's more social than physiological: to be palatable to American audiences, and because of the American vernacular being strongly associated with blues and rock n' roll. You can't sing “ain't nothin' but a hound dog” in any accent other than the original, otherwise it sounds weird. Why do non-English-speaking countries sing in American English? The same reason. Because that's what they grew up with, and to reach the audience that will appreciate their sound.
Rock band Lostprophets are a perfect example. Here's their song The Fake Sound of Progress. They sound very American, but they're Welsh. And the Welsh accent is a very distinct accent. The decision to project an image of being American has clearly been very successful for them.
Now compare with rock band The Arctic Monkeys, the vocalist Alex Turner is from Sheffield, north of England, and has a very distinct Sheffield accent even when singing.
Or Blur. Essex, sourthern England. Very southern accent.
Or Oasis, from Manchester. Very manc accent. Huge in the UK. Not well known in the US.
Or The Last Shadow Puppets. Very northern English accents.
Also compare with rock band Kaiser Chiefs from Yorkshire, north of England. Also very distinct accent and dialect. “Not very pretty I tell thee” is a very northern turn of phrase that would have no meaning outside the north.
Or Pulp, from Sheffield.
Elbow, from Lancashire. Guy Garvey (the signer) sounds just like he talks.
Really, there are a lot of big Brit rock bands you've probably never heard of. I've noted that these are less well known in the US than the UK. Imitating the American accent has a long tradition. The exception to this rule where the English accent is retained is in the punk rock movement starting from the 70's, and a little bit in the Britpop genre in the 90's (e.g. Oasis and Blur) and to a smaller extent in the 2000's (the other bands I've listed above). I wouldn't claim that breaking the US requires having an accessible broad American accent, I'd lean more towards retaining your native accent to be a sign of uncompromising personal pride in where you come from. It takes courage to sing as yourself, and not to imitate clichés you've heard growing up.
I think folk artists tend to embrase their local accents, indeed exagerating the nuances of these accents. On the other hand, pop singers tend to favour a more "international" and polished accent, which makes it more difficult to locate where the singer is from.
Clear Dublin (male) and clear London (female) accent:
Shane Mac Gowan sings with a Dublin accent but speaks with a London accent. :)
More folk songs sung in English:
Clear Irish Midlands accent: - http://www.youtube.com/watch?v=W5fBppsntAE
Clear Irish Midwest accent: - http://www.youtube.com/watch?v=FSU687C38zo
Clear Irish Northwest accent: - http://www.youtube.com/watch?v=owS-yzRDK6k
Clear Dublin accent: - http://www.youtube.com/watch?v=Yg_3t-CHBZs
Clear Scottish accent: - http://www.youtube.com/watch?v=PAD_E1kaYuY
But even in more pop like forms you will hear people embracing local accents:
Very clear English Northeastern accent: - http://www.youtube.com/watch?v=ct-qa6SjRZo
English Northern: - http://www.youtube.com/watch?v=piv0ZK7frnU
Furthermore, artists from non English speaking countries might well "adopt" an accent depending on where their music style is based:
American sounding Swedes: - http://www.youtube.com/watch?v=XEjLoHdbVeE
English sounding Swedes: - http://www.youtube.com/watch?v=S_q8L8Tksd8
Americans have very long open vowels when speaking so when they sing the don't sound very different.
You guys can argue all you want on this topic but I think it's true.
Some people read this and probably didn't want to believe it because they thought it would be an insult to their accent to sound American, but it's not necessarily sounding American - it's just having long open vowels when you're singing, which you're supposed to do. Americans just happen to speak like that.