Of course, anyone who's been in the system for a long enough time can probably tell you that. If a healthy person goes to 7 different psychiatrists, they might receive 7 different diagnoses. If that drug didn't work, let's try this one, etc.
That said, throwing away the DSM entirely might not be the answer. While there are numerous reasons why somebody might have specific symptoms, there have been a variety of efforts to understand the underlying nature and reason behind why certain systems might cluster together.
For instance, people with BPD tend to be afraid of abandonment, whereas people with AvPD tend to be afraid of intimacy. This underlying problem results in the symptoms you see listed in the DSM when they're severe enough, so seeing these symptoms clustered together might help you realize the underlying social issue.
This isn't a perfect, one-to-one correspondence, but I've participated in some research that's going in that direction and read a few studies on these correlations. I know some researchers are working together to create a multifactor model based off of the Big 5 and the MMPI, and working alongside neuroscientists to find correlations for the various factors. They're retaining names for specific placements on the spectrum from the DSM.
So if you consistently show up in the tests that you're worried about abandonment, then you rank higher in the spectrum correlating to BPD. If you show up as worrying about intimacy, then you rank higher as avoidant. It's all meant to be focused on those underlying issues that the symptoms stem from, to be used by diagnosticians.
So far, it seems promising. I'm not sure if it will ever become mainstream, though.