Most commercial use of ML, including neural nets, is small data application-specific business logic. Think phishing / spam / fraud detection, anomaly detection, semantic search, image search, keyword labeling, classifying or segmenting customer data. These applications have well-understood business value propositions. Much, much less often the ML application focused on truly large data.
I think we might see a winter in super big applications like self-driving cars or voice assistants, but ML in general is just a boring, non-controversial business tool with hundreds of valuable applications.
You’ll still need statistical specialists to train and operate models and ensure systems avoid pitfalls like overfitting, poor convergence, multicollinearity, confounders, etc.
So I doubt this will have much impact on ML job market. Companies that invest in ML will continue to run circles around companies that don’t. You’ll just see the unjustified over-focus on SOTA neural networks die down and become just another boring tool in the toolbox like everything else in ML.