My opinion is that many many people (especially in the UK) want to like music like the Black Keys but before Brothers they didn't have the cool factor. They weren't really in many magazines except the hardcore ones and basically because the vast majority hadn't been told by radio or by NME that indeed the "Black Keys" are cool, they didn't give them the time of day.
We've had a few things culminate together this year as stated, they've been on the Radio more so the indie kids and none "blues lovers" had exposure to them. We know there are people out there who like Rock n Roll as can be seen by KoL's success and the resurgence of the Rolling Stones and their fans n fans of students who only two years ago would have sneared at dancing to Sympathy for the Devil while out on the ale, and still probably wouldn't be able to name their albums or influences - ooh ooh yea! But the vast majority of their new fans are the same as TBK's they need to be spoon fed and told it's ok to like the Band. Twilight being one major factor, but i also think that "cool" films such as Rock n Rolla/Black Snake Moan etc also helped. Lets be honest besides fans of classic rock, rock n roll, blues, whatever you want to call it everyone else is pretty clueless or scared of admitting they like that kind of music due to their social circles.
I've always said to everyone i know, if i can get you to a gig no matter what music they are into, Dance, R n B, Folk, Radio 1 specials, Pop, if i can get people to TBK gig they will love them especially those who like KoL and other pop rock bands haha. And that was proved when i dragged about 6 of my friends to the Liverpool gig, they loved them. they just need to be guided there and i think twilight and other films have helped do that.
But taking away those things and the new influx of fans who needed to be directed to them I think it's a mixture of awesome riffs and songs which people have been longing for but no one really has provided properly since the 60's/70's. Also it sounds cliche but their passion for the music (which sometimes i worry is dwindling due to the exasperating tour schedule, maybe it's time they slowed the touring down a bit, wrote more material for us 
but also got their gigs in more demand, control the supply and demand factor) anyways i digress, where was i... ah passion and meaning within the tunes, they don't sound forced or fake. Obviously the last two albums have had well known producers involved which has made the music industry seriously take note, and therefore written about but also made their music has become a lot more marketable to people who may not like just a roaring guitar.
The solid fan base that was built up over a long period of time ensures that the band has grown steadily from my first gig which was a packed out Leadmill Venue in Sheffield full of balding men their wives with probably about 50 people my age (probably more but you get the picture) all just nodding along until the last few songs, then I saw them in Leeds Uni, next minute there was a lot more people my age and in their 30's with the balding men and wives at the back. Now since being on WB (which has all the pluses and drawbacks we've spoken about in length here), writing more radio friendly songs and also writing songs which can be enjoyed by people who aren't as into their blues (i know i know) or their rock riffs, guitar overdrive etc etc so the the fan base has become even younger 16 - 18/19 making up most of the "mosh pit" area of the venues lol with us 20 - 30 somethings closely surrounding them followed by our balding friends around the edges and at the back 
The UK is a weird place, people worry about the image of the Band and what people will think of them for likin that Band. It's like an underground thing among students to like Bands and people almost have a contest like i would say have you heard of the Black Keys (3 to 4 years ago when i was in uni) and someone would be like ah man yes no one has heard of them awesome, n they would go have you heard of *insert obscure band name*. so it was sorta cool to like unknown bands, but this has bubbled up now and now its cool to like previously "unknown" bands who really are making it big so it's no longer underground, but people still kid themselves that they are because they aren't always on Radio 1.... haha i hope all that makes sense and you know what i'm trying to get across in this mammoth post.
But to sum it all up, they just have awesome tunes there is no two ways about it, without good songs they wouldn't have got so popular. They have brilliant songs. Put any keys song on and say you don't like it and want to switch it off.... er it would be hard to find one. With other bands i could list 3 at least per album. I think their dabbling with the past but keeping it fresh just works and there is always going to be an audience and fans for that kind of music, hailing back to the glory days 
apologies for the epic post, i ramble, i need to learn how to be concise. x
"When the sweats dried in, It smells like Rock n Roll"
thats how i roll, plagiarise, make longer and worse!
