The old saying is "train your weakness, race your strength". But that doesn't mean neglecting your strong points, not by a long shot. Perhaps doing focused exercises to bring up your weakness (like Greg Lemond doing weekly sprint training even though he is not a natural sprinter) as part of a balanced training program.
For the duathlon training, I don't know much about it except that the guy I was riding with last night says that weekly running seems to keep his muscles in shape for competing in du's while near-daily riding keeps his fitness up for both activities and is better for buggy sweltering summer weather than running. YMMV.