There are groups and companies exploring probabilistic programming as an alternative to CNN and other deep learning techniques. Gamalon (www.gamalon.com) combines human and machine learning to provide more accurate results while requiring much, much less training data. The models it generates are also auditable and human readable/editable - solving the "opaque" issue with deep learning techniques. Uber is exploring some of the same techniques with their Pyro framework.
Having said all of this, we're not arguing that CNN have no place - in fact you can view CNNs as just a different type of program as part of an overall probabilistic programming framework.
What we're seeing is that the requirement of large labeled training sets becomes a huge barriers as complexity scales - making understanding complex, multi-intent language challenging.
Disclosure: I work for Gamalon