People, while typically varied from one another, tend to not be overly "unique". Labels can show the common ground between specific sets of traits.
You misunderstand. Labeling sets of traits can be useful for the very reason you just stated. However, labeling people in the context of a diagnosis tends to carry with it the implicit assumption that those traits are undesirable or 'bad.' Now, in some cases, BPD for instance, it may be helpful to the individual to seek psychotherapy or medicate to avoid acting on suicidal thoughts. But for things like narcissism, sociopathy, and psychopathy, trying to typify the personality not only stigmatizes it to the rest of society, but also lends itself to reductionism. Individuals, whether they have it or don't and are just trying to find somewhere to fit in, tend to try to align their thoughts and actions with the generalized personality traits of whatever PD they're fixated on.
So, my original point about statistics. If we plotted a histogram of personality traits in the population at large, it would look like a normal distribution in N dimensions. 'Normal' or 'Neurotypical' people would then fall within approximately 1 standard deviation in any direction. Sociopath traits would lie in a certain sector, and thus would be 2 or 3 deviations from the norm varying those particular parameters. But just because something deviates from 'normal' doesn't mean we need to treat it as a disorder or assume it's inherently bad or undesirable.
If you are over the age of 18, you don't have to give a fuck if people think it's "bad" or not unless you've thrown your rights away. People also won't find out your disorders unless they're fairly obvious or you tell someone about it. You decide what to do about the knowledge, as it's not like a diagnosis becomes public record.
To be ashamed of your disorders is to be ashamed of your very own traits. Who cares if they stigmatize it? While my own have brought me hardships, they have also made me stronger in other ways, in many cases from learning to compensate for them.
They only truly suck when you don't know how to deal with them, otherwise it's just a burden. To overcome adversity grants strength, while using disorder as an excuse is far more shameful than the disorder itself.
You don't pick what problems you have, but you do get to decide how to deal with them. A person who deals with their issues is not shameful.
Faulty reasoning. Working to change one's own nature is a continuous effort, not one that can simply be accomplished and then forgotten about. Neuroplasticity is a fascinating area of study, read up on it sometime. Perhaps if the person were able to remove all memories of their experiences, they would no longer have issues. But that begs two questions: is a personality disorder a product of environment, genetics, or some combination of the two? And also, how can you categorically define 'issue,' without appeal to moral philosophy?
If the issues were acquired through nurture (such as specific fears), then yes, removing memory could theoretically remove the fears from removing the context in which it originally developed. How likely the individual would be to develop new fears however would still be a problem if they were born with a stronger predisposition toward developing them.
When it's something genetic, nature, it doesn't just "go away". It's what you do about those problems that judges a person's character. Enabling it or denial can make it worse, while facing it can help in gaining a tolerance and an understanding of it, two things required for proper functioning.