Lists like this are never perfect, especially since there rarely is a consensus as to what is best. Some of the selections on this list seem odd, including the selection of BATJ as Haley's stand out. But I can live with BATJ being the song they chose. It was her breakout.
For AI the list underscores that fact that they have been doing this a long time, unlike some other singing shows. It also creates buzz as people argue about who was best. It puts people in a position to say, yeah those are great performances, but how could you leave <insert favorite here> off the list?!?? It's even greater!! So, right or wrong on the selections, the presentation of Most Memorable performances is accomplishing its marketing purpose.
The absence of Moanin' was the first thing I thought about in looking at the list. AI gets a pass because it wasn't a competitive performance but it should get a special mention for being totally awesome and unique. MAE isn't the only one who likes Moanin.