In my opinion, Radiohead has always been more on the eccentric side of "mainstream", at a time when people were tired of the old and were looking forward, they came to the masses. Each release is quite different from the rest and their creativity seems to be what fuels them... after the huge response from OK Computer, I think they simply wanted to push the envelope and move on.
I've seen too many bands who do it right once and then try to feed off those moments again and again to no avail and never take the risk to reach out beyond. At the same time, I've seen even more do something that is just brilliant initially and then never return to expand on or explain further, but rather opt to move so far away that they end up losing what had made them brilliant in the first place...
Now, I'll admit that I have never been a "huge" fan of Radiohead... I did quite enjoy The Bends and OK Computer before Kid A, and I have always respected their interest in expanding the envelop.
I've been a purveyor of experimental and electronic music since the early to mid-nineties and ran a radio show showcasing experimental music for two hours every week for 4 years, so when I first heard about Kid A, well before its release I was very intrigued. I remember when it was first released, how many fans were initially so disappointed, disturbed, and quite frankly p*ssed-off; much like a country fan when they turned the dial to my radio show... out of curiosity, some continued to listen, soaked it all in, and came out the other end with a different and genuine respect/understanding...
As far as influences, I do remember explicitly that they mentioned well before the release that they had bought up the entire Warp Records back catalog and locked themselves in a room. To many this added to the mystery at the time, to me it meant that we were all in for something truly special. Specifically, if you listen to the title track on the album and then Aphex Twin's Richard D James Album the influence is quite obvious. Idioteque, also utilizes the cutup, reassembled, "drill and bass" style beats first introduced by Richard (and friends) with the early versions of the H.A.B. releases, etc... btw, Bjork has always regarded Richard and Warp Records as two of her biggest modern influences and they have collaborated quite extensively.
I guess what I'm trying to purvey with all of this is that experimental music, when done right, creates a truly unique and inspiring experience unlike any other and that these sonic experiences carry over into our everyday lives and leave us wanting more of what we now believe we have been missing. We then tend to worship those who lead us out of our caves; for many this was Radiohead with Kid A...
With the release of Kid A, Radiohead ushered in the masses who already praised their music into a new realm of sonic inquiry and for these efforts, they deserve my gratitude and respect... and that is why I love Kid A so much.