For my movie recommender project, I wanted to support Letterboxd but they didn't respond to any of my emails (they have a closed API). So for now I only support Trakt. If anyone knows how to get onto the Letterboxd API please let me know!
Ideally, yes, to avoid to force the user to enter manually the films he likes... (or, like simiansays did, proposing an integration with another website)