I agree that it is theoretically possible to rotate the radar image
instead of the chart image. In practice however, virtually everyone
is used to looking at radar images in "heading up" format.

There's no theory involved, the E-80 does it. At least from the perspective
that someone that wants to see the radar overlaid on charts can do so while
the charts are being displayed in a 'heading up' orientation. Or if
they're looking at the chart in 'north up' orientation it'll likewise
overlay the radar. We use these two modes all the time.

Uh well, yeah, when looking at *only* the radar scope rings it's rather
standard to see them in heading up format. I think you can show it in north
up mode as well. Although I personally don't see myself ever using it that
way.