Last Impression
ryanhoover.me
ryanhoover.me
That said, I think this piece is not at all relevant to how we use web services today. Case in point: I almost never log out of Netflix. So that is almost never my "last impression" of Netflix.
Instead, what my most recent last impression of Netflix is: after the TV episode finished, I went back to my Netflix homepage, the preview-thumbnail of the next episode looked really amusing...my most recent thought about Netflix is I must get back to my Netflixing tonight.
In other words, if Netflix's homepage designers have done their job right, then the logged-in homepage is the first impression and the last impression of a subscriber...subscribers should almost never see the log out page except in unusual circumstances.
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In the case of Facebook, where we're all likely to log out purposefully for privacy reasons...FB should make the page as non-hostile as possible, but again, most people who log out of FB (which, let's face it fellow HN privacy geeks, is not very many) are purpose-driven in a way that no number of cute animals or fuzzy text will change that. In fact, being too cute will just creep us privacy geeks even more.
One more use case: Google search. Google famously has designed its search offering to get users off of the page and into their destination as soon as possible. If Google has done their job right, then the last impression you have of Google is the blueness of the link that you're clicking. Where in this model would a designed-last-impression fit? A "Come back soon!" modal? Using some of the search result page to remind you how cool Google is? All of these things clutter the results page unnecessarily.
Again, not saying that the OP is wrong to think about this (though I question the interpretation of the sparse scientific passage he quotes), it's just that it's pretty much irrelevant to modern online services' usecases.
More important are the end points in the user's engagement with the product within a particular "session" (as you've noted). This varies by product and for some, there's never a clear jumping off point.