merging non-dimension coordinates with the Dataset constructor

When adding two DataArray objects with different coordinates to a Dataset, a MergeError is raised even though one of the conflicting coords is a subset of the other. Merging dimension coordinates works so I'd expect associated non-dimension coordinates to work, too.

This fails:

In [1]: import xarray as xr
   ...: import numpy as np

In [2]: a = np.linspace(0, 1, 10)
   ...: b = np.linspace(-1, 0, 12)
   ...:
   ...: x_a = np.arange(10)
   ...: x_b = np.arange(12)
   ...:
   ...: y_a = x_a * 1000
   ...: y_b = x_b * 1000
   ...:
   ...: arr1 = xr.DataArray(data=a, coords={"x": x_a, "y": ("x", y_a)}, dims="x")
   ...: arr2 = xr.DataArray(data=b, coords={"x": x_b, "y": ("x", y_b)}, dims="x")
   ...:
   ...: xr.Dataset({"a": arr1, "b": arr2})
...
MergeError: conflicting values for variable 'y' on objects to be combined. You can skip this check by specifying compat='override'.

While this works:

In [3]: a = np.linspace(0, 1, 10)
   ...: b = np.linspace(-1, 0, 12)
   ...: 
   ...: x_a = np.arange(10)
   ...: x_b = np.arange(12)
   ...: 
   ...: y_a = x_a * 1000
   ...: y_b = x_b * 1000
   ...:
   ...: xr.Dataset({
   ...:     "a": xr.DataArray(data=a, coords={"x": x_a}, dims="x"),
   ...:     "b": xr.DataArray(data=b, coords={"x": x_b}, dims="x"),
   ...: })
Out[3]:
<xarray.Dataset>
Dimensions:  (x: 12)
Coordinates:
  * x        (x) int64 0 1 2 3 4 5 6 7 8 9 10 11
Data variables:
    a        (x) float64 0.0 0.1111 0.2222 0.3333 0.4444 ... 0.8889 1.0 nan nan
    b        (x) float64 -1.0 -0.9091 -0.8182 -0.7273 ... -0.1818 -0.09091 0.0

I can work around this by calling:

In [4]: xr.merge([arr1.rename("a").to_dataset(), arr2.rename("b").to_dataset()])
Out[4]: 
<xarray.Dataset>
Dimensions:  (x: 12)
Coordinates:
  * x        (x) int64 0 1 2 3 4 5 6 7 8 9 10 11
    y        (x) float64 0.0 1e+03 2e+03 3e+03 ... 8e+03 9e+03 1e+04 1.1e+04
Data variables:
    a        (x) float64 0.0 0.1111 0.2222 0.3333 0.4444 ... 0.8889 1.0 nan nan
    b        (x) float64 -1.0 -0.9091 -0.8182 -0.7273 ... -0.1818 -0.09091 0.0

but I think the Dataset constructor should be capable of that, too.

Start by running the Dataset constructor reproducer with the two DataArray objects and compare it with xr.merge on renamed datasets. Trace how the constructor handles non-dimension coordinate conflicts versus dimension coordinates; done means the constructor accepts the subset coordinate case and preserves the merged y coordinate without raising MergeError.