I checked the first four search result pages on Web Applications and Google, but I didn't find an answer to my question and issue, which is also discussed on the Google Help forums by other people.
My issue is, I know from people that they might have more than one e-mail address, but I don't remember it, as most people use cryptic e-mail addresses, even older folks. Now when I search for a person, e.g. in this screenshot:
It doesn't help me to display and find the e-mail address of this guy. Important: I might not have saved this e-mail address of him to my contacts yet, thus it doesn't help me to search my Google Contacts! Also, if you don't want me to use Greplin, switching over to Google Contacts is another (time-consuming) step that I want to avoid.
And then of course there is the issue described in the Google help thread: Sometimes I simply want or need to see the e-mail address, even if obtaining it is not the problem.
I checked my IMAP client (Postbox 3), but their search is actually worse in regards to my goal.
Conclusion: As I am using several browser extensions that alter and expand the display and features of Gmail, I wonder if there isn't a browser (Chrome) extension also for this issue?