Thanks for this post, and link to the WAPO article--guess I haven't been imagining this, then! The tiled radar layer is just painful to watch load.
The radar.weather.gov server may not be the issue since it loads the ArcGIS base maps fairly quickly. But the radar layer is served up by the open data server at NOAA--so this is probably the bottleneck.
Regardless, the deprecation of Flash has been pretty obvious for years. There was more than enough time to budget for and develop a suitable replacement.