I would think if you depend on data stored in a container being persistent, it's an indication you really should be mounting a volume to the container and persisting the data there. Then container restarts won't matter. Best practices are generally for containers to be "cattle" instead of "pets", and data persistence usually has a different solution.

Regarding using a container for distributing static site generators, does anyone really do that? I think you may be building up a straw man here, I haven't seen anyone recommend this workflow. Could you elaborate on how this relates to the parent comment's mention of using less space when running many containers? What the parent comment mentions is, in fact, highly relevant to some of the main use-cases of containers, which is running many containers of the same service on one or many hosts. Space can be saved there with layer caching.