use level of a MultiIndex for plotting?

[mathause]

It would be nice to be able to use a level of a MultiIndex for plotting.

MCVE Code Sample

import numpy as np
import xarray as xr

da = xr.DataArray(
                  np.random.randn(10),
                  dims="x",
                  coords=dict(
                              a=("x", np.arange(10, 20)), 
                              b=("x", np.arange(1, 11))
                              )
                  )

da = da.set_index(x=["a", "b"])
da

This creates the following DataArray

<xarray.DataArray (x: 10)>
array([-1.34516338,  0.97644817, -0.24032189, -0.70112418, -0.8686898 ,
       -0.55607078,  0.56618151,  1.62847463,  0.84947296, -0.5775504 ])
Coordinates:
  * x        (x) MultiIndex
  - a        (x) int64 10 11 12 13 14 15 16 17 18 19
  - b        (x) int64 1 2 3 4 5 6 7 8 9 10

Is there a way to plot a line using one of the levels of the MultiIindex?

da.plot(x="a")

returns

ValueError: x must be either None or one of ('x')

da.plot()

returns

TypeError: Plotting requires coordinates to be numeric or
dates of type np.datetime64, datetime.datetime, cftime.datetime
or pd.Interval.

(which makes sense). If da is a 2D Variable the error is

ValueError: x and y must be coordinate variables

Expected Output

A line plot

Versions

Output of `xr.show_versions()`

INSTALLED VERSIONS

commit: b3bafee
python: 3.7.3 | packaged by conda-forge | (default, Jul 1 2019, 21:52:21)
[GCC 7.3.0]
python-bits: 64
OS: Linux
OS-release: 4.15.0-91-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8
libhdf5: 1.10.5
libnetcdf: 4.7.1

xarray: 0.11.1+335.gb0c336f6
pandas: 0.25.3
numpy: 1.17.3
scipy: 1.3.1
netCDF4: 1.5.3
pydap: installed
h5netcdf: 0.7.4
h5py: 2.10.0
Nio: None
zarr: 2.3.2
cftime: 1.0.4.2
nc_time_axis: None
PseudoNetCDF: installed
rasterio: 1.1.0
cfgrib: 0.9.5.4
iris: None
bottleneck: 1.2.1
dask: 2.6.0
distributed: 2.6.0
matplotlib: 3.1.2
cartopy: 0.17.0
seaborn: 0.9.0
numbagg: None
pint: None
setuptools: 41.6.0.post20191101
pip: 19.3.1
conda: None
pytest: 5.2.2
IPython: 7.9.0
sphinx: None

[mathause]

For the line plot it is here:

xarray/xarray/plot/plot.py

Lines 37 to 38 in b3bafee

	if x is not None and x not in darray.dims and x not in darray.coords:
	raise ValueError("x " + error_msg)

For 2D plot it seems to be here

xarray/xarray/plot/utils.py

Lines 370 to 371 in b3bafee

	elif any(k not in darray.coords and k not in darray.dims for k in (x, y)):
	raise ValueError("x and y must be coordinate variables")

Both might need something like this:

any([x in da[dim].variable.level_names for dim in da.dims])

or maybe

any([x in da[coord].variable.level_names for coord in da.coords])

?