I'd love to see this implemented too! I can't think of any other background-running/Menu Bar app that doesn't keep running when the main app has been QUIT.
I have the same problem. CMD+Q is a reflex for me when I done with something. Having to remember each time I'm done in Enpass's Main Window to use CMD+W instead of CMD-Q is problematic. It's even worse for my Dad, who's a 20th-Century guy and after finally training him to QUIT apps he's not using, I've had to train him "except Enpass, just close the window in Enpass."
A short, off-the-top-of-head list of apps whose background processes continue to run after quitting the main app: 1Password, Dashlane, Sticky Password, Little Snitch, Fantastical, Dropbox, MalwareBytes, Day One.
In fact, off the top of my head, I only know of two other apps one other app with a main window and a MenuBar or background process that don't leave those background processes running when the main app is quit: Evernote and TickTick. (Although I'm sure there are others.)