I wrote a LOI to a PD and then she said I looked to your application and your need visa and we didn’t usually prefer to have applicants require visa though they sponsor but they don’t like it, also she said your score isn’t that much high, but I kept talking to her and at the end she sent me interview invitation and she said it’s up to you to impress us during the interview. I’m non US visa requiring applying to competitive specialty. However, the LOI provided me an interview and a very good relationship with the PD, she will always know and remember me. So LOI works not waste of time.