I tend to agree with most of your thoughts.
I am not quite sure that Kanye is the most influential artist since 2000, but I think the two records of his on this list clearly deserve to be on the list, in the order where they were ranked and with the spacing between them. Was My Twisted a top 20 album of all-time? I do not think so. But, it certainly was a top 50-100 and is representative of his best work.
The guy is crazy as hell and in certain ways he is not musical like say The Beatles or Prince or D'Angelo or (insert name of artist that actually plays instruments), but his sound has been tremendously impactful and of mostly excellent quality since his first album.
Sgt. Pepper and the White Album were better than The Beatles stuff listed ahead of it, which were also great albums. Just not as good. I am not sure how the White Album went from nearly always being the #1 record ever to somewhere in the top 50 over the past 20 years. Nothing around it truly changes, but I guess the perception of it has changed.
I completely agree on Radiohead. OK Computer, In Rainbows ... I even think that Hail to the Thief was better than Kid A, which is a great record, just not their best.
Really surprised that The Dark Side of the Moon is so low.
With Kendrick Lamar, I think good kid, m.A.A.d city was his best record, but To Pimp a Butterfly was more socially relevant given its timing. Both excellent, as was DAMN.
I do not think those OutKast records deserve to be on this list. Speakerboxx/The Love Below generally has been regarded as their best record. And really, it is The Love Below, if anything they have made, that deserves to be on this list.
Reasonable Doubt was a great record, but it pales to The Blueprint, I think. Jay Z has always been great at proclaiming things and having people go along with it. It is a great talent of his and he has always talked about Reasonable Doubt (which is a very good record). But, The Blueprint was easily his best and should be on this list.
I think 1999 is better than Purple Rain, but sort of like with Kendrick, Purple Rain was more socially/culturally significant.
Finally, Drake had best playlist records than Take Care. If You're Reading This Its Too Late is probably his best work (and most controversial).