A good deal of the argument seems to be that a) specific past moral panics, like pinball, turned out to be harmless b) worrying about smartphones shares some similarities with worrying about pinball c) therefore smartphones, like pinball machines, are harmless, and it's irrational to worry about them.
But that argument simply doesn't hold. The thing about "moral panics" is that you retroactively apply that term to things that groups were worried about that seem silly in hindsight. But people also worried a lot in the past about drug use and rising obesity, which both have turned out to be gigantic social problems.
Even leaving aside the validity of the studies (I think that Haidt overstates his evidence at times), I think people can come to conclusions just by introspection and observation as to whether the impact of smartphones/algorithmic content on society is more comparable to pinball or to a new drug.