If David Barton’s work has been widely discredited, why has he remained so popular and influential?

Barton's work has been largely discredited since he started in the 1980s. I remember discussing his work with a college roommate who majored in history back around 1989. Suffice it to say that he wasn't impressed. I never have been, either.

I think a lot of it is that Barton's been able to create his schtick in parallel with academic institutions, getting funding and support from outside among people (regrettably including a lot of conservative politicians) who really ought to have known better. But he was useful (yes, cue up Lenin's term for that) to them, so he was allied with them. It's more or less a parachurch organization that proceeds by word of mouth communication.