What political objective is accomplished by not coddling children?
What the various kinds of "avoid coddling" types want is determining the details of what should be allowed to traumatize them, specifically, in order to shape society.
As far as I understand all Haidt calls for is to remove the boundaries that have been established over the past couple of decades, or what selectivity are you hinting at here that are part of that supposed plan to shape society?
More generally, the discourse tends to boil down to "I was spanked and I turned out fine!".
Yes, there is an inconsistency in his writing regarding why social media specifically is something we should protect children from. But Haidt is not suggesting that a return to a corporal punishment regime, or anything like it, is desirable. His concerns are things like free play, independent movement, negative (not only positive) interactions and so on.