I think whether or not a 'label'/diagnosis is appropriate for your daughter is impossible to say over the internet.
However, I agree with you that it isn't always necessary or beneficial to seek a diagnosis. It depends entirely on the severity of the symptoms or condition and whether or not anything can be done to help.
A few years ago I had a girl in my class who was very classically aspergers (I know aspergers doesn't technically exist any more but I find it such a useful differentiator from autism. If it's an unacceptable term I apologise). When I first raised concerns with her parents the response was : "Do you have any academic concerns about her?" I said no. They then asked "Will diagnosing her as aspergers help her with her social difficulties?" I had to say again, probably not. So they didn't want to explore it. Because she was just who she was and there was nothing that could have changed her so why bother going down a long, hard diagnosing road.
However, had that child had a condition that could have been improved, then I would say that not seeking a diagnosis would have been very unwise and unhelpful.
Interestingly, I also work in a Sunday School class where we are not allowed to know personal details about the children (excluding medical danger). At first, as a teacher, I was appalled that I couldn't know about any diagnoses - 'how am I supposed to teach and support them without knowing any challenges they might face?' I thought. But actually, it's fine. I suspect I deal with 1 child with ADHD and another two with ASD but, even though I don't know for sure, I can still treat them as they need to be treated.
Sorry that was a bit longwinded but, in short, I'm on the fence.