With small amounts of data and/or unconventional learning situations, there should be options for incorporating domain expertise in interesting ways. I might be wrong, but I think the fraction of problems that can be solved with deep learning/large data set analysis is a small fraction of the set of AI problems as a whole.
For example, at a statistics symposium at MIT last year Stanford Professor Robert Tibshirani mentioned a healthcare (cancer diagnosis) problem, done in collaboration with healthcare people: http://www-stat.stanford.edu/~tibs/ftp/canc.pdf (these slides are different from the ones used at MIT, the content is similar though). He mentioned how they talked to some deep learning experts at Google, who told him that the data set was too small for effective deep learning usage. Another reason is mentioned on pg 30 of the above, basically sparsity being more important than nonlinearity here.
In healthcare, people care a lot about "interpretable" models. The term is ill-defined, but in a sense it is something where the trained model is easily explainable, and easily written down. A linear model is a simple example of such a thing, though usually insufficient on its own. Deep neural nets arguably do not meet this, hence a reluctance (among other reasons) to shift in certain fields.
Your point may still be valid though - I do not know whether there are enough viable economic opportunities. Computer vision in particular is dominated by DNN/large scale analysis these days, and I sympathize with your difficulties here.