How many initial positions would be "strictly" needed to avoid opening preparation?

The first google result for "number of chess openings" cites the Oxford Companion to Chess which has 1,327 openings listed. Let's assume that each new starting position has this many openings associated with it. Let's assume each opening consists of an average of 10 moves.

An extreme example of what human memorization is capable of is Akira Haraguchi who has publicly recited 111,700 digits of pi. Let's assume that memorizing a digit of pi is an equivalent effort to memorizing a move in a chess opening.

That would mean that after (111,700/(1,327*10)) = ~8 opening positions, having a comprehensive knowledge of opening preparation would be an achievement equal to Haraguchi's mastery of pi.