I read that there was a mid-air collision recently and the NTSB's response was to issue an Advisory reminding us all to look out the window, like we used to. (I confess that, with all this neat stuff in the cockpit, I'm not looking outside as much as I used to in the old days.)
To that end, should the Quick View box time out and close itself, say after 5 or 6 (or 10?) seconds of no selection or last selection? (Or the Option to set it up that way?)
That way, after you've seen the Quick info you wanted to see (dialed in a freq, checked the wx, etc.) you could put your eyes back outside, knowing that the box will close itself automagically. (There could be a "Hold" button where the "Done" button is if you need to keep it open. ("Done" not being necessary, since the box would be Done after x seconds.)) This would be like an option on some custom ROMS on Android that offer to close the Quick Settings panel or Notification shade for you after making a selection.
It only saves a second of your time - but who knows? A second might save your life.