This is semantic baggage to me. Identity is best loosely held, and it's mostly determined by our actions. There's no real faking, just acting in accordance to, or against, one's preferences.
Colloquially when people use the term "fake it till you make it" they don't really mean "pretend to be a different person". They just mean act in the face of uncertainty. You can do it with or without undeserved confidence, it's besides.
I tend to agree with you, but there’s another saying: “play to your strengths”, because people don’t all have the same potentials. I think it’s healthy to always strive for self improvement, but going with the grain of one’s personality is easier and likely to land in a better place. That’s the message I take from “be yourself”, but I have to admit that it does ring a bit hollow when one is young and hungry.
Colloquially when people use the term "fake it till you make it" they don't really mean "pretend to be a different person". They just mean act in the face of uncertainty. You can do it with or without undeserved confidence, it's besides.