This happened to me a few days ago.
That won’t always provide a solution because there is often good reason to use the search box.
My situation: I had just suspended a troll who had one common IP address across several accounts.
I entered the IP address in Admin > Users search box and hit Show Emails to check whether there were any common points between email addresses, to help ID him next time by checking any suspicious new signups (he switches naming style & IP pretty effectively, but only when he realises it’s necessary).
I then went to backspace the IP from the search box in order to enter the other last-known membername he had, because this:
Clearing the search box showed emails for all currently active users, just like the full list sorted by Last Seen at Admin > Users and illustrated here.
Began typing in name of one of his earlier accounts, call it Troll-1.
While typing that, all members who share T and Tr and Tro and Trol (etcetera) in their Name, Username, and email addresses, a largish number on the forum, were also being updated with each character typed.
Like a lot of forums (example posted by someone here) many of our users have certain common words significant to the forum’s topic within their Name, Username, or email.
Sometimes there is a case for running searches on a name liked by the troll to see how many members share them, before hitting Show Emails - but without wishing to go in and out of that page to clear it.
For a moderator who’s attempting to eradicate a troll but otherwise pressed for time (many of us are volunteers), having to go in and out of the same page just to close the displaying of emails, when they otherwise need to check several accounts with a common link, that is not ideal.
This would solve the problem and remove the need to spend time going in and out of the same page whilst investigating the same person. 