Although it can't be calculated like this, it doesn't mean that the formula of rotational energy comes from this. You can look at the derivation of the formula of rotational energy in college physics books. Definitely not ∑ V22mi * 1/2. It has its special equivalent calculation method and derivation process. You think too much.
Get to the bottom of the hole, or your question will be untenable. I still think you should read the textbook first. Don't stick to a college physics textbook. I believe that there are many versions of textbooks that will clearly demonstrate the derivation process of rotational energy formula. For example, we studied the college physics of Wu Baishi of Jiaotong University and wrote it well.