Ideally, it should be possible to display that as entry content, and search it.
However, there are two independent parts to this: saving the entire page, and extracting content from it to a usable form (can be done later).
There are other things we can do aside from saving the HTML, e.g. save additional content like images, or request the page is saved by the Wayback Machine (and not save the content in reader), but these seem like overkill.
Maybe custom plugins that don't have a concept of "full content" should be able to opt out.
Some feeds don't have the full content in their entries. I would like to save the full content for a specific entry for archival/search purposes.
Related:
Some thoughts: