There was a podcast that Mendes was on a few years back, and he conceded that Man of War was actually the Bond theme for Spectre for a few days. Someone on the crew recognized the song (as Radiohead had never actually recorded the song in a studio but toured it live back in the 90s), and it got removed because it was not originally written for the film (which would invalidate it for the Oscar for Best Original Song).

The podcast is linked below, but it seems like they don't have it available to stream currently.

https://www.bbc.co.uk/programmes/b09clppp

It wasn't necessarily that Spectre was too moody of a song, it was the fact that Sam Smith provided Writings On The Wall between Man of War getting removed and Radiohead coming back with Spectre. The production team had already lined up their theme song for the film when they got offered Spectre, and they didn't think they had heard anything that changed their mind (which is crazy to me).

It definitely explains why Godrich said it was all a waste of time.