How should Dataset.update() handle conflicting coordinates?

Recently, we updated Dataset.__setitem__ to drop conflicting coordinates from DataArray values being assigned if they conflict with existing coordinates (https://github.com/pydata/xarray/pull/2087). Because update and __setitem__ share the same code path, this inadvertently updated update as well. Is this something we want?

In v0.10.3, both __setitem__ and update prioritize coordinates from the assigned objects (e.g., value in dataset[key] = value).

In v0.10.4, both __setitem__ and update prioritize coordinates from the original object (e.g., dataset).

I'm not sure this is the right behavior. In particular, in the case of dataset.update(other) where other is also an xarray.Dataset, it seems like coordinates from other should take priority.

Note that one advantage of the current logic (which is violated by my current fix in https://github.com/pydata/xarray/pull/2162), is that we maintain the invariant that dataset[key] = value is equivalent to dataset.update({key: value}).

Start by tracing the shared code path between Dataset.setitem and Dataset.update, then read pull requests 2087 and 2162 for the conflicting-coordinate behavior. Done means deciding which object’s coordinates take priority while preserving or intentionally revising the stated assignment/update equivalence.