Looks nice! This is definitely something that I've missed from mne_analyze :)

A few high level thoughts/ideas offhand:

1. Do we have to be careful / think about the interaction with brain.plot_sensors (which can plot a helmet)?
2. I wonder if a more future compatible API might be brain.add_evoked(evoked) and brain.add_field_map(map). Just trying to think a little bit more generally, someday we might want to have for example brain.add_inverse(...), brain.add_evoked(...), brain.add_field_map(...) and the object can automatically "do everything it can": apply the inverse to the evoked and plots the STC and the field map. But I guess this could also be done via brain.add_inverse(inverse, evoked), too, so maybe overkill to go this direction.
3. Or even better -- rather than make Brain more and more complex by adding bits of code from other places, I've been hoping that at some point we could implement a proper plotting event/publisher-subscriber system (see https://github.com/mne-tools/mne-python/wiki/GSoC-Ideas#2-event-system-for-brain-and-evoked-plots). If we did, it seems like the functionality in this PR could be achieved by something like the following I think:

   brain = stc.plot(...)
   fig = mne.viz.plot_evoked_field(..., fig=brain.figure)
   brain.connect('on_time_change', fig.set_time)
   

   and you could get the benefit of also connecting a mne.viz.plot_evoked_joint(...) or plot_evoked_topo if you wanted those to update, etc.

Even if (3) seems like a better way of accomplishing this (and it might not!) then it doesn't necessarily have to stand in the way of this PR. But if you were motivated to work on getting the event system started... :)

(3) sounds like the way to go if we want to add even more capabilities to Brain. The file is too large and complicated as it is already. This event system sounds like a good way to achieve some of the todo items in this PR. Notably, it would be nice if the field patterns can still be plotted with our time viewer, but without a FreeSurfer brain mesh in the center (like xfit can). This is clearly out of scope of the Brain object.

it would be nice if the field patterns can still be plotted with our time viewer, but without a FreeSurfer brain mesh in the center (like xfit can).

Agreed. I think an event system could make it much easier to provide xfit-like interactive dipole fitting for example...

Should we start building an event system to allow this sort of stuff (maybe over the next month or so?), then see if we can get the equivalent functionality of this PR, or would you rather get some version of this PR in as is? I don't want to make perfect the enemy of good here, what you have is already cool and usable!

See #11678

Closing for now. I'll re-implement this when the ui-event system is operational.