issue_comments: 238053437

I would suggest putting the logic to create new variables for levels in the private _get_virtual_variable in dataset.py. We already call this function for creating variables on demand in operations like ds['time.month'], so it's already called in all the right places (even in ds.coords, and so on). We could simply extend it to also check for MultiIndex levels and build those variables on demand, too, but only when necessary. If possible, it would be nice if ds['time.day'] works even if time is a multi-index level.

This could get us most of the way there, but there are still a few things to watch out for: 1. What happens when you write ds.coords['level_1'] = ...? With the current implementation, I think this would create a new variable level_1. In an ideal world, maybe this would replace the MultiIndex level? For now, it is probably better to raise an error and note that the MultiIndex should be modified instead. 2. Should levels appear in ds.keys() or ds.coords.keys()? If we're printing them in the repr as peers to dimension coordinates, then maybe the answer should be yes? It could be confusing to have both the redundant levels and the multi-index coordinate in there, though. So maybe it's simpler to avoid changes here.