I had a brief conversation with Fr. Jerry Thompson about didacticism in art. The problem is always a thorny one, and I have written about it before in the context of Aristotle. (You can read that here.) Since I'm once again traveling through a Tillich phase, it might be helpful to re-address the issue using some Tillichian vocabulary.
For Tillich, there is a difference between categories of aesthetic knowledge and other types of knowledge like ethical knowledge. (Here, he is obviously following Kierkegaard.) In Tillich's ideal theonomy, the conflict between autonomy and heteronomy are transcended. The artist creates in freedom without strictures and proscriptions from heteronomous and authoritarian sources. However, the artist creates work that has meaning and context for the community without the prohibitions that are intended to keep him/her within communal bounds. The didactic art works that we don't like are the works were we can see the autonomy or heteronomy poking through the cracks of the formal structure. That is, content and form become separated from each other in inferior works. The entelechy of a superior work fuses form and content into an ontic whole that can be separated for pedagogical ends, but in real the life, form and content can't be separated without damaging the work. So, let us assume that a specific work of art contains a piece of ethical knowledge as part of its content. A good example might be something like Picasso's Guernica.
I wouldn't suggest that the ethical knowledge is the whole of its content, but it does remain a significant piece. It would be reductionistic to suggest that the painting (the form) is simply a coffee cup that is holding a liquid (the content) which is moral outrage at the horrors of war. In a similar fashion, there is a danger on the other side. You cannot solve the problem (as some have tried to do) by emphasizing the form at the expense of the content. The painting is about something. However, it is not about something in the same way that a coffee cup is about serving as a device to carry coffee. I can just as easily fill my coffee cup with a 12 year old Tomatin. In coffee cups, content can be interchangeable. In masterworks, content and form are eternally fused. As we move down toward inferior works, the tension between form and content becomes readily observable because the two forces are in tension.
In one case, the structure of the form is not sufficiently appropriate to bear up under the weight of the idea of the content. The normal result of this end of the spectrum is sentimentality.
In the other case, the lack of profundity in content is communicated through clear formal ideas and we get propaganda.
In many ways, the theological analogy that Tillich is hinting at is the incarnation. We can speak theologically about the differences between Jesus as human and Jesus as God, but anytime we start pulling apart the paradox, we get into Arianism or Docetism.