no, not really just

We have a lot of information about Chet Baker available ... Starting with his music, through the interviews and going until Webers "Lets get Lost". All of it leaves us with am imagination of the person he may have been (agreed, it is the last episode of his life and may be distorted through that).

What I get from all this is the idea that that Chet Baker was a introverted, slowly hesitating and careful person.

From a biopic you could expect to be drawn from the (maybe imaged) character of the person that is being pictured.

And if you related what we seem to know about Chet Baker, it is obvious "Born to Be Blue" does not pay enough respect to that.
Some of the shots are good mis-en-scene. But the pace is way too fast. And so is the Hawks interpretation: he moves too fast, speaks too fast, everything seems to be too 'proactive'.
He show like a nervous kid, being thrown around in arbitrary situations and trying to act accordingly, instead a man who has detailed doubts about life and such.
One thing Chet Baker could do very well is to hide is nervous condition pretending to look 'cool'. He was trying to be bold, trusting his instincts.

I wish the makers (and Hawks) would have listened to Chet Baker music and got their inspiration from it.

The timing for the voice interpretation of "my funny valentine" (trumpet is okay) is so wrong. It is so rushy. It misses that made Chet Baker unique. It is a perfect reflection on what gives the whole movie the wrong feeling.

This movie (and Hawks facial expressions) should have been moving much much slower ...And then it could have been a good movie ...