Yeah but her behaviour/treatment of you has been significantly less than acceptable for a happy relationship.
Negligence is legitimate grounds for a split any day.
You being a bit 'cold' if you think that is what it is not the problem, it is part of the solution.
What you are being is determined. Determined to make a fresh start and a clean break. She has had plenty of chances (the on and off again nature of the relationship) to alter her behaviour.
I have had a similar break-up and while in my own mind I wavered and was a little hurt, I knew that being 'cold' was the right thing.
My ex in that relationship begged to get back together, to forgive her, and so on, and while I had no intention of being mean or cruel on the outside I had to be firm and appear to be totally and completely convinced. For myself so that I would accept it was over and believe it, and for her, so that she didn't have false hope for a hopeless relationship in which I couldn't trust she would really change.
You have been more than fair and you explained yourself fully to her.
Now unless you're more than 97-8% convinced she can actually change or the relationship has a chance, save both of you the grief and stick to your guns and move on.
Its your life and your relationship so ultimately do what you think/feel you should do, but in my mind it is better to be happier single than miserable together.
Best of luck OP.