Oooh Hand in Hand, good track but like dmg has said certainly one of the weaker tracks from the album...
Hand In Hand, judging by the views and listens on various platforms seems to be on the same level of popularity as Solid Rock, and Les Boys seems to be far less popular, however, this song had quite a back story which Mark told before playing the song live. That may be a clue.
My take is that the absence of a live version of this song is a combination of many things: unpopularity, cheesiness ('The sky is crying the streets are full of tears / Rain come down wash away my fears', I mean...), the absence of story that you can tell before the song, the fact you're already playing 6 songs from the album live, the fact that the arrangement is quite elaborate, I mean nobody can say they never tried to play it!
I never encountered Mark talking about this song in interviews, and personally, I always thought, honestly, that it was co-written with his brother David. And especially this line: 'how come my love is so strong?' is so David. I always thought they had the song credited to both brothers, but I was wrong. But maybe he won't play it because of some sort of David connection?
Anyway. I think it was just a combination of things, not a single one, as it always happens, same with Tunnel Of Love and other songs famous for MK not playing or abandoning.