I'm sure it's pandering to the audience. Most of the audience know almost nothing about musical theatre, so the show offers them songs they can sing along with rather than stuff they've never heard.
I don't believe it when Andrew Lloyd Webber says "I'm judging it on this performance". They already know which of the contestants are inferior, so I suspect that out of sight of the cameras it's a matter of "This one has the acting talent of a spoon; if you get the chance to get rid of her grab it with both hands" or "Keep that one in whatever it takes". The whole point of the sing-off is to give the show a chance to save an otherwise promising candidate from the consequences of a poor public response, so it would be stupid to base the elimination on a single song.