There are different, additional, objections to that. For example, it would make life rather difficult for market makers, which would mean a lot of the liquidity would dry up, which means the spread would widen out, which means trading would be more expensive.
I think there is scope for designing market mechanisms which have the volatility-reduction effects of periodic auctions, but which still allow market makers to hedge. I hope people are working on those.
And how is that a bad thing in and of itself? It would presumably knock out some of the ultra-low-margin HFT but so what? If it would have the effect of turning the stock market into less of a roulette table, with fewer gamblers compared to bona fide investors - isn’t that a good thing?
I think there is scope for designing market mechanisms which have the volatility-reduction effects of periodic auctions, but which still allow market makers to hedge. I hope people are working on those.