bear in mind those songs didn't even exist as radiohead songs until after the album was finished and they asked clive to join the live band. they were thom yorke pieces he was intending to use with afp or solo, and the band never even tried recording them during the limbs sessions, only for the tour, so by asking them to be included, you are basically saying you want the limbs studio album to be a 2012 (or later) release, and then everything else would've been delayed too and we could expect radiohead to start recording lp9 sometime later this year.

it's like saying the bends should have included talk show host, or pablo should have included the trickster. also, while staircase has a pleasant groove, fans idealize it simply because it is not on the album and therefore has no studio version, and everyone prefers live radiohead to nigel-produced radiohead. but if you had the studio version of staircase you'd probably dislike it because it would be about as close to slick middle-of-the-road whiteboy funk/r&b as they've done, much closer than house of cards and lotus flower studio versions, and many people don't like those already. the basic lyrics and melody of staircase are just much weaker too and that's probably why they never even considered it as a possible album song. it's basically a fun exercise for them to play a song like that, to show their chops as a live band. it's a jam rather than a song, and frankly their chops could use more work on the basis of that jam. it is good but not great. it has the flaws of many AFP songs, in the sense of being not as funky as it wants to be. it just isn't as good as over half the songs on king of limbs, it would be one of the weakest songs on there, maybe even the weakest. daily mail is better, that's a great song, but even that would not be one of the best songs on limbs (it's not as great as bloom, lotus flower, codex, gutg and separator) and because of its lyrical and musical differences from other songs (the more obviously political lyrics, the ok computer/thief-like nervous rock climax) it would not necessarily fit well on limbs and it might detract from the musical and lyrical statement the album is making.

you don't just throw every good song on an album and it automatically improves, just like you don't make a good mix by just putting every song you like on it. and there have definitely been times in the past, like amnesiac and the bends, where a radiohead album actually excluded songs that- unlike staircase and daily mail- were inarguably better than some songs they included, but maybe did not fit the things the album was expressing. with king of limbs, they didn't even exclude the best songs they had. you say staircase and daily mail are "arguably the best songs they released in 2011" but come on, you only feel that way because you are idealizing their obscure fans-only status, like those ridiculous people who claim in rainbows disc 2 (which only even has six actual songs) is way better than in rainbows.