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

Chess 960 uses, well, 960 and this seems to solve completely the problem. The issue is that some of those positions can be quite messy, specially if you want to play some variant like crazyhouse 960.

Instead, I have played a few games (both chess and ZH) with this method: the same rules as 960 , but the king and queen are kept on their original squares. This allow only 32 positions, but these look way more "natural" (specially for castling). A few times I have played using starting positions with rotational symmetry, too, as in shogi, making them 64.

Would those 32 (or 64) positions be enough to nullify opening prep, for strong players?

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.

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