intereresting theory here
i do notice a correlation between myself and others cutting their hair after a shaking event such as a breakup. but it doesn't have to stop there. it could be about a death of a friend/loved one, any life changing event really that the person cares about.
for me personally, it symbolizes change. as simple as that. "i am changing my hairstyle because my life around me is changing". its a way of expressing myself outwardly when inside i'm still trying to deal with everything. it's not necessarily that i have become more independent, but it definately is like "cutting" myself off from something. in that case, a relationship.
edit: so based by your theory would it work vice versa for girls w/ longer hair or are wanting to grow their hair out? as this is what i'm trying to do now and consider myself in a 'comfortable' relationship.