The benefit isn't that big.

From the standpoint of writing quality code, I think it is better to use the background page instead of LocalStorage in that it lets you avoid writing to disk (which requires space and has worse performance than using memory, although at this scale the difference is trivial) and doesn't pollute your LocalStorage namespace as much.

An advantage of the LocalStorage approach is your readers can write code in a way similar to how they would if you were not writing an extension and it makes the material more accessible in that it requires less understanding of how Chrome extensions work.