Not necessarily true that MLPs are very compute expensive. It is maximum a couple of layers and if your input is sparse (categorical) you can gain even more. For some problems it can be the fastest and decent non linear model from my experience.
I don’t think that was the claim… MLP/ANNs are fine except for the difficulties around interpretability. DTs and LR are preferable on that front. Or an SVM if you know a kernel/similarity metric that kills it in your data.
