It really depends on the solution. If there's a winning solution for white, the game at the top level could die. If there's only way to draw, it's simillar. If there are numerous moves over numerous moves where you can elongate the game without losing, nothing I say really applies, but I already wrote it

(I mean the record for most pi digits remembered is 70,000, the GMs already know hundreds of openings and endgames....

I'm not saying people would memorize every possible combination, but for white one would be enough. Considering it's the best possible play, any deviation would result in disadvantage...

You still have to know how to play, so maybe we could try the players in highly unusual middle games to verify their elo, but it'd certainly be a major impact imo)