There has already been very interesting discussions on 'If its possible" for korra to reconnect with her past lives ( I am of the opinion that she can) But I havnt come across a discussion on "if she should". I am of the opinion that this would be best. I have already mentioned that, as Roku explained to Aang in The Avatar State, one of the biggest strengths of the avatar is the all of the knowladge, and power that comes from all of the avatars past lives. Plus, no one can really teach an avatar how to be an avatar except for a past avatar (I used the word avatar way to many times there).
That being said, Korra has started a new era in which the central role of the avatar (being the bridge between the spirit and human world) is now not needed, and it could be argued that the past avatars couldnt really contribute anything to this new era since its fundimentally different from thiers. The exception to this would be Wan, since he lived with spirts for so many years and learned how to live in harmony with them.
What are your thoughts? should the past be forgotten, should korra look only to the future? or are past lives fundimentally important to being the avatar?