Well I was thinking the exact same thing on Monday at the RAH.
This is my observation....... during the rest of the show, the songs run into each other or pause for a few words from the band. After TGGITS, there is it seems a deliberate pause and the house lights are raised slightly - the audience react at this point with applause. So it's not so much the audience showing more appreciation, it's the fact that the show pauses to allow it?
However, it always moves me and I for one am happy to show my appreciation at this point. Additionally, I have seen this happen at both DG's and RW's shows - so it seems to be the norm. Also on this point, Mica Paris failed to perform it to anywhere near the standard of Amy or Ola, it is a technically difficult thing to do as Clare Torry was improvising, so they have to practice and practice to reproduce her original vocals. A lot of singers don't seem to be able to get this just right, so when an audience hears it faithfully reproduced, it strikes a chord.
So when you add all these things up, you can see (or to me you can) why it happens. It is a very popular and moving piece of music and when performed well reduces many people to tears. It's quite a personal thing too and depends a lot on how much it moves you on an emotional level.
GG