Actually you totally buried the question. Exactly where did our original poster ask about vector analysis or centripetal force? His question assumed that mass was a part of the equation that he was not interested in.
If you are going to make claims here it would be wise to ensure their correctness.
The original post was over 5 years ago. some time before I actually joined SF.
I did not in fact join the discussion until recently, when I did indeed offer a novel answer to the OP's question "Where did the half come from" in my post#39.
If you are actually interested to learn anything you might be interested to know that there is another energy formula containing the factor of one half.
Strain energy = 1/2 stress x strain.
This also causes difficulty when folks first meet it.
I think both these difficulties are caused by over emphasis of the formula work energy = force x distance in early learning of physics.