Ensuring units agree is indeed a form of type checking. A more thorough procedure for the former is dimensional analysis.

I think the fact that action and angular momentum have the same units played an illuminating role in making sense in Bohr's model regarding why only certain orbits are allowed.

Not sure how that would play out once angle is considered a fundamental entity.

This sure is a rabbit hole.

Thanks for your submission

https://news.ycombinator.com/item?id=49372847

hope it gets picked up.