Firstly, I live in Australia so I'm speaking from that perspective.
I think that if you need a diagnosis then you should get one, but if you don't need it then don't. Really as an adult the only reason you would need a diagnosis is if you are so dysfunctional that you need it to qualify for services, benefits or support. In Australia, just being AS will not qualify for anything, you're assessed on function, not a diagnosis.
If you're having difficulty in certain areas, then treating them individually is probably the better way to go. Diagnosis is easier for children because it gives them access to services, and schools etc. to funding for them. They cater more for children to give them a better start so they may avoid the pitfalls later, as a preventative. From 16 years these cease to be relevant.
Doctors vary from one to the next, but most good doctors wont give you a diagnosis unless they believe it is medically necessary. Not because you don't present the features, just because you don't need it. They would be more inclined to treat the individual areas of difficulty for at least 2 years without success before considering it, and then may not if they don't think there would be a benefit. Under medical terms, you can have 2 heads, 6 arms and 10 legs. If you were born that way then that's fine. It's only if it's a problem that matters.
If you want it so you can be officially in the club so to speak. I can understand that there is some validation there, but the truth is there is no club. A diagnosis will general just confirm others' biases, not change them. If you can't see the “monkey tree”, when you say something everyone stares at you with their mouths open, you constantly get accused of things you didn't do, and constantly get into trouble for doing exactly what you were told to do, now you know why. You don't need someone's approval. Being born was your certification.