Yes and literature is a pretty bad way to teach critical analysis. My high school did political speeches from history and that segment was infinitely more enjoyable than The Scarlet Letter.
You can just teach the thing you want to teach.
The problems with teaching symbolism using novels are:
1. Novels considered “curriculum-approved literature” often have symbolism that is irrelevant to a student’s life. It was placed there intentionally by the author, and was blatant to all readers when it was published, but it is indistinguishable to a student from the teacher making things up.
2. Teachers who aren't the best end up teaching from a “it's true because it's true” mindset, which may as well be “because I made it up and said so.” These are quite common.
3. Or the teacher draws from a pool of stock symbolic and thematic answers for all novels. Astute students will spot that immediately and treat it as a game of guessing the teacher’s answer rather than engaging with the text.
Sure, and there are plenty of classes that use different written forms for their pedagogy. An advantage of novels is that their length often allows for different thematic depth and complexity and their narrative can make it easier to hold a reader's attention through that length.