I sometimes think that fans over-analyze what Ayu does XD.. I think she just did it to add effect to the song/concert and that she felt like it :p Kind of a repeat of A museum. She just wants to give a good performance (imo).
A Song for XX with acapella was 10x better than talkin' 2 myself and her voice carried much more meaning.
Also Rule acapella for AT09 doesn't really seem to serve any role than as concert opener. (it does seem cool though~)
Buttt with that said.. I like waterballoon's explanation too