Broadcasting doesn't respect scalar coordinates

Usually if I apply a broadcasting operation to two arrays, the result only includes values for coordinates present in both. A simple example:

In [160]: data_array = xarray.DataArray(dims=("x",), data=[1,2,3], coords={"x": [1,2,3]})
In [161]: data_array.sel(x=[2]) * data_array
Out[161]: 
<xarray.DataArray (x: 1)>
array([4])
Coordinates:
  * x        (x) int64 2

However if I do the same thing but select a scalar value for the x coordinate (.sel(x=1)) yielding a scalar coordinate for x:

In [164]: data_array.sel(x=2)
Out[164]: 
<xarray.DataArray ()>
array(2)
Coordinates:
    x        int64 2
In [165]: data_array.sel(x=2) * data_array
Out[165]: 
<xarray.DataArray (x: 3)>
array([2, 4, 6])
Coordinates:
  * x        (x) int64 1 2 3

Here the result includes values at all the coordinates [1,2,3], all of which have been broadcast against the scalar value taken at coordinate 2. This doesn't seem correct in general -- values from different coordinates shouldn't be broadcast against eachother by default, even if one of them is a scalar.

I would expect this either to result in an error or warning, or to select only the corresponding value at the scalar coordinate in question to broadcast against, resulting in e.g.:

<xarray.DataArray ()>
array(4)
Coordinates:
    x        int64 2

Reproduce the scalar-coordinate and one-element-coordinate examples from the issue, then trace xarray's broadcasting and coordinate-alignment entry points to determine where scalar coordinates are handled. Done means the behavior is explicitly resolved for this case—by an error, warning, or coordinate-aware result—and the examples have regression coverage.