I studied computer vision in grad school when these were some of the state of the art methods, like the Mumford-Shah segmentation model and various inpainting models that set up the problem basically as a calculus of variations problem over the appropriate Sobolev space of image intensity functions and/or discontinuity-permitting boundary functions.
I’ve worked as a practitioner in computer vision as well and I think I disagree with your “under taught” comment.
In practice, the variational methods are not competitive at all with deep learning models, and even very naive transfer learning can apply better inpainting or segmentation than the older variational methods.
It is already merely a footnote in the history of computer vision. In 10 years it won’t even merit being part of literature reviews.
So for many applied domains of ML, I think spending roughly zero time on these variational methods in schooling is a good idea. You can always come back to them later, but you probably won’t need to.
A different application domain, variational Bayesian inference, might be a case where there is more reason to care. Although, things like ADVI are more about one very fixed approach to the problem (minimizing KL divergence to find a best approximating distribution from a class with known differentiability properties), and only in novel research would knowledge of general variational techniques give much value.