I noticed that I couldn't open Minecraft Launcher a few days ago, so went into the macOS Activity Monitor to see if it was open. To my surprise, the Launcher had been running since I last opened Minecraft the day before.

After force-quitting the Launcher, it allowed me to open it. Now, every time I want to play Minecraft, I have to open the macOS Activity Monitor and force quit the Launcher. 

It seems like the launcher stays open even after it has launched the game, albeit in a non-responsive form.