I don't know why boxing the frame isn't a good idea. Making the frame more rigid makes the frame stronger. That is why frames are boxed in and crossmembers are added.
Rigid is not always stronger. The original frame is designed to flex some, and that's OK.
If you box a portion of the frame it will still flex before and after the boxed part, possibly more so. The transition from boxed to open may cause problems or grow cracks.
Give it some thought before haphazardly changing the design and operating characteristics of a frame. Personally I think it deserves a lot of thought and some structural/mechanical engineering background too.
Semi trucks don't have boxed frames and they carry lots of weight for hundreds of thousands of miles.
There must be more to a simple C-channel frame than meets the eye...
Grigg