I'm just speaking from zero knowledge really, but maybe 'All Day' has something to do with the later Smiley Smile song 'Whistle In'. Did you ever notice that song is very similar to the melody to the chant of "wah wah ho wah" in 'I Love To Say Da Da?'
"All day, all night, all day long, whistle in".
I could be, and probably am completely off on this. But it's fun to speculate, even if it yields nothing real.
It does seem to have the same melody as Wa Wa Hoo Wa from Da Da. But every time I hear it, I can picture the trumpet then Mike singing "today could be a lot of fun...". The piano parts in each song seem to have the same rhythms if not the same melody. I'm musically illiterate, so I have no idea what notes or chords are being played in each, or what the progressions are, or anything like that. I'm just going by what my ears are "telling" me.