Should there ALWAYS BE a period after the middle initial?

"Several widely recognized style manuals provide guidance in favor of using the period. According to The Chicago Manual of Style all initials given with a name SHOULD "for convenience and consistency" be followed by a period even if they are not abbreviations of names. The U.S. Government Printing Office Style Manual states that the period SHOULD be used after the "S" in Harry S. Truman's name."