Using LP, comments can be arbitrarily formatted, with TeX equation handling, beautiful figures, tables, cross references, indices, table of contents, etc.

Code can be presented in a way that best suits the reader (versus the writer or the compiler). Though Knuth's examples usually seem to dive right in, lacking the introduction to be provided by the latest stuff in TAOCP.

When I use it, I write it like a paper decorated with code, where the code can be extracted and run. I usually include the necessary make file and perhaps some test data. Entries in figures/tables are sometimes generated automatically by the program being described.

There are lots of old papers and critiques about LP, by Knuth and others. You should check 'em out.