> This is the definition of a strawman.
(Actually, it is an example of a strawman.) Anyhow, rather than a strawman, I'd rather us get right into the fundamentals.
1. Feed-forward NN computation ('inference', which is an unfortunate word choice IMO) can provably provide universal function approximation under known conditions. And it can do so efficiently as well, with a lot of recent research getting into both the how and why. One "pays the cost" up-front with training in order to get fast prediction-time performance. The tradeoff is often worth it.
2. Function approximation is not as powerful as Turing completeness. FF NNs are not Turing complete.
3. Deductive chaining is a well-studied, well understood area of algorithms.
4. But... modeling of computational architectures (including processors, caches, busses, and RAM) with sufficient detail to optimize compilation is a hard problem. I wouldn't be surprised if this stretches these algorithms to the limit in terms of what developers will tolerate in terms of compile times. This is a strong incentive, so I'd expect there is at least some research that pushes outside the usual contours here.