In my mind, there's two points to Stan. The first is the actual math -- it can fit lots of models, much faster and more flexibly than other alternatives. The s

In my mind, there's two points to Stan. The first is the actual math -- it can fit lots of models, much faster and more flexibly than other alternatives. The second is to go out and meet the practitioners where they are. That means making Stan models look like the equations in your paper. It means connecting to existing research software ecosystems. It means making it easy to adapt. In this case, if you end up tightly coupled to, say, specific R data structure then it becomes much, much harder to make it also work well for Python, and for Stata, etc. Additionally, it means that if I start on a model in Python then I cannot easily switch to using R (or vice-versa). Using a DSL also has the nice property of cleanly separating Stan world vs R world. That makes it easier for users to build an accurate mental model for what happens when/where, which hopefully then leads to better performance. Most importantly though, Stan code is incredibly concise and clear for specifying models.