I know that \begin{center}\end{center} cause excess white space so it is always suggested that \centering should be used which I use all the time. What would ever justify the use this tag?

Maybe if you want a title (non official) at the top of a page?

What I mean is that you have a document and on page 3 you are going to discuss the 3 body problem whereas you were on topic about the 2 body problem previously? Or would another environment suit that better still?