Those who say that they like overly attached girls don't know what they are asking for.
Those who say they don't mind or like an overly attached girlfriend either had or currently have a relationship with an overly attached girl only for a few months or they are currently single or never actually had a girlfriend.
For a few months, yes, an overly attached girlfriend is not that bothersome, but after 6 months of being together, it's just as good as being in prison. Just a figure of speech, of course.
However, the funny thing is that even if you already find your life boring being with an overly attached girlfriend for a long time, then you decide to break up with her, you'll still feel very miserable and very very sad after the break up, if you actually loved her, that is.
I recently just broke up with an overly attached girlfriend. I made a mistake and she is the one who decided that it would be the best if we break up for a while, for the good of both of us. Another factor that led to our break up is that she went home crying and her parents advised her to keep our relationship down for a while.
Just as what happened to me, the best way to get rid of an overly attached girlfriend is to make a mistake so that the girl will be the one proposing to break up. but that would be very bad for your ethos.