That is true but then your average drunk would still choose the path of least resistance which is usually the nearest bush, wall or tree. We are genetically wired to look for the easiest solution which would of course be peeing wherever we are when nature calls. The only thing that stops us from exhibiting this behaviour when sober is inhibition. When alcohol numbs our inhibitions and sense of risk we revert to our most primal selves and in some cases that means we piss in places we should not piss in.
Not having meetings or conf calls might work for you but I would be very surprised if it works for your customers and/or peers (assuming you have any).
If there is one thing I have learned it's that the quality of communication in a team usually makes or breaks the project. The quality of communication with a customer makes or breaks the relationship.
It's important to remember that humans have been communicating for thousands of years without email, chat servers or telephones. Our brains are hard-wired to respond to facial expression, tone of voice and body language.
German cities are full of public urinals such as the ones you describe. The problem is that they are quickly soiled making them unappealing, even for the most drunk revellers. The only way the behaviour can be curbed is with big fines - it works in the UK for the most part.
Since most of my time is spent slouching over my laptop I use Sundays to escape to the outdoors. Having a dog is a great excuse to explore the wild and the fresh air clears my mind.
If it rains, I still try to avoid TV/Laptop in favour of getting creative in the kitchen or having a few beers and banter with friends.