Morbi
Scavenger
Dr. Mario is Mario, Lucina is NOT Marth.
Here is the first portion of that quote that refutes your fallacious sentiment.Strange, I wonder why Lucina is her own character after the invention of alternate costumes... oh wait... Sakurai blatantly asserts why that is the case! Silly me, always forgetting!
However, even though Lucina shares her physical stats and techniques with Marth, the characteristics of their attacks differ. When two such similar characters function in an even slightly different manner, I give them a separate spot on the roster since that will affect battle records and whatnot. In that sense, you could say she was very lucky to join the fray!
Initially, I had considered including Lucina as one of Marth's alternate costumes. After all, she has a close relationship with him in FE:A. In such cases, even if two characters' names and voices differ, as long as they function the same way, I assign them as alternate costumes. The Wii Fit Trainers, Villagers, and Robin are examples of this setup.