Given that, why should we return to the world where the father had great influence rather than abandon all the memes and ideas that remain that rely on that power disparity?

Well, firstly, there are all the fully general Burkean arguments. Not sure if those Burkean arguments can't likewise apply to the more established aspects of the "modern" family, though - it often fails, but it works even more often. E.g. traditionalists complain - loudly - both about single motherhood and two working parents... yet the second innovation doesn't seem to directly wreck anything.