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The experience shows that cooperating and communicating computing systems, comprising segregated single processors, have severe performance limitations. In his classic "First Draft" von Neumann warned that using a "too fast processor" vitiates his simple "procedure" (but not his computing model!); furthermore, that using the classic computing paradigm for imitating neuronal operations, is unsound. Amdahl added that large machines, comprising many processors, have an inherent disadvantage. Given that ANN's components are heavily communicating with each other, they are built from a large number of components designed/fabricated for use in conventional computing, furthermore they attempt to mimic biological operation using improper technological solutions, their achievable payload computing performance is conceptually modest. The type of workload that AI-based systems generate leads to an exceptionally low payload computational performance, and their design/technology limits their size to just above the "toy" level systems: the scaling of processor-based ANN systems is strongly nonlinear. Given the proliferation and growing size of ANN systems, we suggest ideas to estimate in advance the efficiency of the device or application. Through analyzing published measurements we provide evidence that the role of data transfer time drastically influences both ANNs performance and feasibility. It is discussed how some major theoretical limiting factors, ANN's layer structure and their methods of technical implementation of communication affect their efficiency. The paper starts from von Neumann's original model, without neglecting the transfer time apart from processing time; derives an appropriate interpretation and handling for Amdahl's law. It shows that, in that interpretation, Amdahl's Law correctly describes ANNs.