This paper was really interesting and it's awesome, but I'm tired of everyone saying that this means parameter counting is a useless heuristic for the complexit

This paper was really interesting and it's awesome, but I'm tired of everyone saying that this means parameter counting is a useless heuristic for the complexity of a model. The more parameters you add to some ML models (for instance NN and SVM) the higher the VC dimension, and that's that. Many models are simply not constructed in a way that a single parameter can encode all of the necessary information. (And still be a continuous function of that parameter)