Sorry,I have to stand up against this particularly.
I don't consider myself either a fully open-minded or a very old-fashioned person. If you want to break down and dismantle the old system of classification and rules, that's okay, I won't object, but the point is what about afterwards.You can't just destroy everything and leave it there.You have to rebuild a new system, otherwise chaos and troubles will spread from social humanities, morals, culture, religion and even to the legal realm.
The same is applied for sexual orientation and labels. Society will not progress because of the disappearance of labels. What society needs is the advancement of the label system. For example, in the situation you mentioned, the current label is more advanced and precise than the previous, and there is a good term is used to label this kind of group that you describe,namely pansexual.
All in all, I think labels are indispensable and essential for respecting yourself, expecting others to respect you, and reminding yourself to respect others.