Well, yeah, that's true of all normal websites too. That's precisely what web crawlers are for. If there's no index page that links to all pages, or some way of iterating through all the pages, you wouldn't be able to exhaustively archive any web site.
Not exactly. While you may miss data that isn't requested specifically, you can crawl the site and get most/all that is accessible through links at least. Stuff only available through search results won't show, but if it's discoverable through browsing, you can get it.
The same can't necessarily be said for custom interfaces that are JS heavy, possibly with non-link click actions, custom sliders, a graphical representation of a map that expects a click on a region, etc. An old style page that lists all the regions (like states, or counties in a state), or even that has a dropdown in a form? Those are much easier to crawl and archive.
> presumably JSON or CSV
That's presuming a lot. Even if it's accurate for most/all NYTimes infographics today, it doesn't mean it's accurate tomorrow, and it isn't accurate today for a lot of other sites.