The aim of this paper is to discuss and draw attention to a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was reported recently in (Darwiche, ECAI 2020) to facilitate model-based supervised learning but it can be interpreted in a causality context as follows. One can compile a non-parametric causal graph into an arithmetic circuit that supports inference in time linear in the circuit size. The circuit is non-parametric so it can be used to estimate parameters from data and to further reason (in linear time) about the causal graph parametrized by these estimates. Moreover, the circuit size can sometimes be independent of the causal graph treewidth, leading to tractable inference on models that have been deemed intractable. This has been enabled by a new technique that can exploit causal mechanisms computationally but without needing to know their identities (the classical setup in causal inference). Our goal is to provide a causality oriented exposure to these new results and to speculate on how they may potentially contribute to more scalable and versatile causal inference.