It becomes tiresome to see the same, tired, mythical versions of the past recycled, sometimes deliberately (because it is in someone's interests to do so), sometimes inadvertently (because the bad pop history people often read other bad pop history as their sources), despite being the sort of thing that a quick correspondence with any expert (even in a forum such as this!) should clear up pretty quickly. For some topics (like, say, the bombing of Hiroshima) the myths are very widespread, much more so than academic understandings that are by now decades old. It does get tiresome to try and correct them.

On the other hand, anyplace where the public knows about something already, and what they know is wrong, can be a nice opportunity for the academic historian to show their worth and to do the ever-appealing "the secret history of X" sort of thing.

I think bad pop history (there is good pop history) is only really damaging when it warps people's understandings of the present and future in dangerous ways. So on some topics I am fine with it. Nobody outside of the academy would even give a damn about what Heisenberg and Bohr talked about in 1943 if it wasn't for Frayn's Copenhagen, and people getting that wrong doesn't actually do any damage to the present world (and gives me an endless conversation starter). Whereas if you badly misunderstand the history of slavery and race relations in the USA, it does do damage to how you interpret contemporary politics, how you decide to vote, etc., and that sort of bad history is often promoted maliciously by people trying to manipulate others.