That being said, I don't understand why HOT would interfere with a hypothetical mechanism for marking index pages as all-visible. If a tuple gets a HOT update, I think the index values should remaing unchanged? And if they do, shouldn't their visibility on an all-visible index page remain unchanged as well?
Unrelated: Thank you so much for your work on "UPSERT" :)
A much simpler way of putting it would be that deletes would have to touch indexes if summarized visibility info was stored in indexes, even in cases where overall there is hardly any benefit from putting per-page visibility information in index pages. It's not impossible to make something like this work, but it's not obviously compatible with the current design.
I'm glad that you found UPSERT useful.
There is one small inaccuracy in your summary, which is that a structure called the visibility map summarizes if a heap page is all visible; that's how index only scans work. At no point do we mark an index page as all-visible, because a HOT update would invalidate that.