I suppose it depends on each individual and the severity. The two people I know who have a diagnosis of BPD were both frustrated that they didn't get a diagnosis for many years (in one case, the psychiatrist had diagnosed it but not told the patient and the patient found out through requesting records). One I'm very close to, my aunt, has been very mindful after getting the diagnosis. Maybe the diagnosis isn't accurate and she isn't what you typically see with BPD, but for her, she appreciates being able to see the patterns. I personally think that I have a personality disorder that hasn't been diagnosed (in my case I would guess it's NPD--although again maybe not as you expect it stereotypically), and I can't say with certainty that it would hurt my rapport with my therapist but I would like to think it wouldn't. He's not big into diagnoses with anything, though (his usual question is: What would it change if you had X diagnosis?). As far as my psychiatrist, I don't think she deal with personality disorders. I can't see how she would be able to given the way she has her work set up. From an outside point of view, I think that if you could see these ingrained patterns and realize what they were, it would be very helpful especially if you could find and resolve the root cause. Or at least make some internal progress.
As far as the person misdiagnosed with bipolar who actually has BPD, I think again that's a function of our system being set up for med-checks and assuming that everybody who walks in the door has a biological issue. Around where I live, it would not surprise me for someone with a personality disorder to see a psychiatrist and leave with a prescription for Xanax.
The interesting thing is that it's not just psychiatrists who seem reluctant to diagnose personality disorders, though. It seems that psychologists don't delve into that too much either, especially with the focus on CBT. I feel as if the people who were the most oriented to treat or at least recognize personality disorders don't exist much anymore (psychoanalytic psychiatrists). I don't know if they would be the best at treating it, but given the etiology of personality disorders, it seems that they would be the most receptive to the idea of personality disorders. The diagnoses are in the DSM which is always being tweaked, so somebody must be doing some research into these conditions. But who is treating them? That I don't know.