It's a simple litmus test and while it generates many false negatives, there are almost zero false positives.
EDIT: At least, for biomedical papers... can't speak for other fields
I prefer to read a paper or article by its merits. E-mail from the author had little impact in that sense.
(Speaking for areas outside biomedical papers, for those, I don' know.)
It's not very difficult to establish a peer-review ring when you use freely available emails, and journals are increasingly aware of this [0,1]. That's why I'm often suspect of journals who let this slide, because it's a sign they don't screen very well.
In 2017, in light of the widely successful and low-barrier ways to game the peer-review system, I don't buy your "leaving an institution" argument.
Corresponding author is more commonly the professor than the main author, and faculty at academic institutions almost always have "e-mail for life" privileges.
[0] https://www.washingtonpost.com/news/morning-mix/wp/2014/07/1...
[1] http://www.nature.com/news/publishing-the-peer-review-scam-1...
For instance, take the Annals of Emergency Medicine (http://www.annemergmed.com/). More than 50% of corresponding authors use gmail.
It's way to easy for journals to fall prey to peer-review rings when they accept email addresses that are easily spoofed [0].
[0] https://www.washingtonpost.com/news/morning-mix/wp/2014/07/1...