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An extreme case of this: working with a synthetically-generated dataset where samples follow a "template" (e.g. bAbI), and manually hard-coding that template into your NN architecture
Fitting parametric models via gradient descent, unsurprisingly, works best when what you are fitting is already a template of the solution. Of course, convnets are an instance of this (but in a good way, since their assumptions generalize to all visual data).
So methodologically, papers making a claim of architectural generality need to demonstrate this generality across a range of tasks and datasets. This is what the ML community used to do before the arrival of these large and expensive dataset-based tasks
Basically yes, researchers should focus on measuring generalization rather than performance on a single task. The point of an architecture innovation is to be able to reuse it across tasks / datasets -- so you should understand what priors it contains, what its specialization is
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