Without opening up a whole argument about semantics, it's pretty idiotic to talk about albums of the 00's without including...00. For example, the decade might end with 1980, but 1980 is still in "the 80's".
Besides, we're using arbitrary marking points to separate eras of recording which really aren't there. Is the music in 1999 so different from 2000, or 2000 from 2001? It's ludicrous to discount Kid A from nomination from such a technicality. Personally, I don't think Kid A is even close to perfect, though I'd consider voting for Amnesiac (and yes, I know this is an unpopular opinion, though people are too idiotic to admit had Amnesiac come out first they'd like it better instead, and BTW the Amnesiac version of Morning Bell's emotional transcendence totally trumps the cold paranoia of the Kid A version).
I read this thread title as 2000--present, which is what most people would assume.
Also, as much as I love Blur, no way either of their last two are perfect or close to it. They're too experimental and creative to settle for perfection, if that makes any sense. The same goes for Peter Gabriel, though I would say Us (from the 90's, I know it's disqualified) is pretty close to perfect.
I won't argue with Neutral Milk Hotel. One of the best suggestions so far.