I think so. Jpeg is an enabling technology just like classification using neural nets. The interface is relatively simple in both cases, the applications are plentiful. Some meta data needs to be supplied to make sure the results are optimal. Both are quite complex under the hood and would require ample study in order to re-create them or in order to fully grok how they operate in every detail. But for high level applications - even if such knowledge would give you an edge - that in-depth knowledge is not a 100% requirement.
The big difference is that jpeg creation with default parameters works fine for probably > 99.9% of use cases. A jpeg encoding the picture of a car will be just as fine as that of a cat. This is not at all the case with the current state of ML, as the originator of this thread has also pointed out with their example.
But there is actually one more problematic area for jpeg: encoding of graphs, drawings etc. with a limited color palette and straight lines. Here, jpeg artifacts become more visible, and to reduce them, you can either turn up the quality, or use a better approach like svg or png. For this, at least a bit of more technical knowledge is required. How many non tech-savy people do even know about svg or png?
But an even more appropriate comparison with ML would be to ask how to improve jpeg to better deal with straight lines. For this, you clearly need to understand the maths.
The comment you originally replied to points out all the ways in which the deep learning "interface" is not relatively simple, at least not if your problem has any sort of deviation from the most simple use cases. For a user, making a jpeg is a one-time one-command affair. If you think training a neural net can be reduced to this level of abstraction (with the knowledge we have today), you have either never used them in practice, or you've been very lucky with the complexity of the problems you've encountered so far.
