It's not that you can't go to the lounge, you just have a 50/50 chance when you pass through a doorway that it will be the lounge :P
Why would we care if monitors have identical serial numbers?
Now, when your system wakes up from sleep, how does it know which one is which? The workaround is to use the port they’re attached to, but that isn’t always might even both be attached to the same port.
I'm not being facetious, that's the monitor issue precisely (while also being completely not).