While the vast majority of post-punk bands who have an obvious taste for the blues seem to enjoy taking the style apart and messing around with the bits and pieces, the Black Keys are the (relative) traditionalists within the subgenre.
With their two-piece, no-bass format, there's no room for clutter or wank, and the raunchy fuzz of Dan Auerbach's guitar (and drummer Patrick Carney's production) owes more to the Gories/Blues Explosion/White Stripes school of aural grime than anything else, but look past all that and the Black Keys are a straight-up blues band who could probably cut an album for Alligator if they were willing to clean up their act and fill out the lineup.
And Alligator would doubtless be glad to have 'em -- the Black Keys's wail is hot, primal, and heartfelt, and Auerback's lean but meaty guitar lines and room-filling vocals drag the blues into the 21st century through sheer force of will without sounding like these guys are in any way mocking their influences.
In short, if you're looking for irony, you're out of luck; if you want to hear a rock band confront the blues with soul, muscle, and respect, then Thickfreakness is right up your alley.
Points added for the fact that the Black Keys performed, recorded, and produced Thickfreakness all by their lonesome in a single day -- further proof these guys are not messing around.