Though agreeing with your evaluation, BTNYC, the technique need not be naturalistic or accurate in lighting and shading, perspective, anatomy, and so on, to have a gravity and clarity worthy of sacred subject matter. Look at almost any medieval illumination - those of Hildegard of Bingen, for instance, though it wouldn't be difficult to find examples of non-naturalistic representations in stained glass or sculpture. I'm sure you know what I mean; but I never knew you had any personal interest in art, and I'd like to hear you expand on what you've said already.
You're quite right, of course... And one might well add eastern iconography to the list. Not naturalistic, strictly speaking, in the post-renaissance understanding of the term, but I wouldn't hesitate to say that those artists were still striving for (and achieved) a "naturalism" of a sort. Those works are still beautiful - harmonious, balanced, dignified, and exceedingly well-composed - despite the artists' not yet having discovered more advanced techniques of reproducing how the eye perceives nature (foreshortening, a thorough knowledge of anatomy, etc.). As such, I'd heartily recommend study of those older styles to students of art who struggle with those advanced techniques. The OP might greatly benefit from such study.
My own background in art is not much to speak of. As I mentioned, I honed my skills (such as they were) by studying comic books - specifically the trash that was on the newsstands in the late 80's and early 90's (quite possibly the nadir of that already very low art form). I attended a high school here in New York that specialized in commercial art and which had churned out a few well-known comic book artists in its long history. Sadly, however, by the time I was a student there, the old methods of training - which treated commercial art like the skilled trade it once was - were all but extinct. A decidedly hippieish atmosphere prevailed, which treated any stupid scribbling as "artistic expression" and little to no actual training in actual techniques occurred. And no one needed that kind of discipline more than the undisciplined doodlers that made up the student body - myself as much as anyone else.
In college, I'd abandoned art in favor of electronic music, in which I achieved some small measure of success. But the less said about that, the better. Suffice it to say that, after college, I had my reversion back to the Faith (or rather a conversion, since I never really had the Catholic Faith, properly speaking, to begin with). I abandoned the music as being incompatible with the Faith (which it was), and, after a few years of struggling to undo decades of bad influence on my draughtsmanship (and my lack of formal training) - which consisted mainly in studying the works of the Renaissance and Pre-Raphaelite masters, as well as reprints of art instruction books by commercial art old timers like Jack Hamm and Andrew Loomis, I found myself not particularly enjoying drawing anymore. Soon afterward, I was gainfully employed in a "normal" job and then married and a father, and all of that put an end to all of my "serious" artistic pursuits.
I never developed the skill necessary to tackle the monumental task of depicting Our Lord, Our Lady and the Saints, so I never dared to seriously attempt it. So, now, drawing has become for me what it was when I was a small boy - simply a fun and relaxing pastime; and something that I am at least skilled enough in to pass down to my children. And, if they show both the ability and the inclination to pursue it, I shall not make the mistake of allowing them to develop their skills by imitating bad art.