I think one of the main reason they “sound“ convincing (though the readers' ignorance is also a necessary condition) is motivated cognition: the kind of people who read such books would like to believe what they say. Lose that, and your strength as a rationalist kicks in. (And anyway, I don't think Chopra et al. are idiots; they are either misguided or bullshitting the readers for fun and profit.)

And what if they sound convincing on a topic you have no expertise in

I'd have to test that. Anyone willing to give me a few paragraphs of either something “serious” or crackpottery (or a spoof à la Sokal), without telling me which it is, about a topic other than physics?