Dataset constructor always coerces 1D data variables with same name as dim to coordinates

What is your issue?

Whilst xarray's data model appears to allow 1D data variables that have the same name as their dimension, it seems to be impossible to actually create this using the Dataset constructor, as they will always be converted to coordinate variables instead.

We can create a 1D data variable with the same name as it's dimension like this:

In [9]: ds = xr.Dataset({'x': 0})

In [10]: ds
Out[10]: 
<xarray.Dataset> Size: 8B
Dimensions:  ()
Data variables:
    x        int64 8B 0

In [11]: ds.expand_dims('x')
Out[11]: 
<xarray.Dataset> Size: 8B
Dimensions:  (x: 1)
Dimensions without coordinates: x
Data variables:
    x        (x) int64 8B 0

so it seems to be a valid part of the data model.

But I can't get to that situation from the Dataset constructor. This should create the same dataset:

In [15]: ds = xr.Dataset(data_vars={'x': ('x', [0])})

In [16]: ds
Out[16]: 
<xarray.Dataset> Size: 8B
Dimensions:  (x: 1)
Coordinates:
  * x        (x) int64 8B 0
Data variables:
    *empty*

But actually it makes x a coordinate variable (and implicitly creates a pandas Index for it). This means that in this case there is no difference between using the data_vars and coords kwargs to the constructor:

ds = xr.Dataset(coords={'x': ('x', [0])})

In [18]: ds
Out[18]: 
<xarray.Dataset> Size: 8B
Dimensions:  (x: 1)
Coordinates:
  * x        (x) int64 8B 0
Data variables:
    *empty*

This all seems weird to me. I would have thought that if a 1D data variable is allowed, we shouldn't coerce to making it a coordinate variable in the constructor. If anything that's actively misleading.

Note that whilst this came up in the context of trying to avoid auto-creation of 1D indexes for coordinate variables, this issue is actually separate. (xref https://github.com/pydata/xarray/pull/8872#issuecomment-2027571714)

cc @benbovy who probably has thoughts

Start by reproducing the behavior with the Dataset constructor examples in the issue, then compare it with expand_dims('x'). Trace the constructor path that classifies a 1D variable named like its dimension. Done means data_vars={'x': ('x', [0])} preserves x as a data variable without implicitly creating a coordinate or index.