The problem isn’t primarily with Evangelical art, it’s with Evangelical theology.
More specifically, it’s with the crummy theology of creativity and creation most Evangelicals have inherited, which sees all media as neutral vehicles for communication. The pulpit, the radio, the book, the movie, the rock anthem - all identical. Valuing these things only for their instrumental, rather than including their intrinsic, value voids artistic media of any real interest, literally shuts off the ability to sense them as art. All human creativity, all matter, all texture, all sound, all smell, all metaphor is reduced to being a sermon illustration.
This, coupled with a crummy ecclesiology, which sees the church primarily as the ear-house (an information distribution multi-purpose cafetorium) without sacred, set-apart, beautiful space, blurs the lines between the culture and the church to the point that one cannot tell where the church begins and the world ends. There is no “inside” the church, because there is no core except the communication. And if the communication is turned up loud enough, the church extends to infinity. Thus, the pastor turned big-tent-preacher turned radio-host turned writer-director isn’t a new/innovative/unexpected outgrowth of Evangelicalism, it’s entailed in the default theology itself.
But the output (because of the problem with the view of art), is, understandably, arid/didactic/inhuman/charmless.