I think there are two key solutions for a resolution here:

1) CDNs are a tried a true method for getting content closer to the end user, properly cached, and for less cost.

2) Expose more services that NOAA and the NWS delivers as APIs. If you are providing services for the public good where the consumers are just scraping Web pages to gather the necessary data and content, then you are doing it wrong. It sounds to me like they are serving more API type content over Web pages than they are Web content to Web consumers.

I don't want to second guess the NWS/NOAA technical architects, because I know they are probably doing the best they can. Someone simply needs to communicate these goals and solutions to the political appointees...