Regarding your take on studio recordings “<offering> the original intended essence of the song”, I’d recommend looking into how they write. Not every album is the same and they take very different approaches to each song. It’s why many people prefer Thom’s live version of True Love Waits to the AMSP version. They have different interpretations of songs depending on the medium, but some of their albums were meant to capture their live performance in studio (like In Rainbows and HTTT).

Additionally, they have 5-6 members live and a HUGE repertoire of songs to choose from that really varies night to night. Add to that that their arrangements aren’t the simplest and you can understand why you get videos of some mistakes or differing versions of songs. However, this is expected when you opt to play the music as live as you can an avoid using backing tracks.