And then notice that removing road signs, traffic rules, etc. is a big change that makes people think. In a place that currently has no rules, you'd probably see better behaviour if you did introduce strict rules.
For example, I once tried to cross a busy street but didn't plan my route properly (like I would do here) and got stuck. Couldn't move forward or backwards and traffic was coming to me. I was worried for a few moments, but then I noticed that traffic just flowed around me. No horns, no near accidents, no panic, just normal flow.
Here are some European examples:
in Drachten Intersection
* * *
Bonus - Jaywalking restrictions don't work:
Contrast with Australia where any intersection of even mild traffic (say within a suburb) has a roundabout to control traffic flow, and all decent traffic intersections have lights etc. Speed and red light cameras are everywhere, everyone uses indicators all the time for everything etc. It sounds overbureaucratic but it means that you can drive around and know what each other driver is likely to do. In contrast, the (apparent) unpredictability and what seems like an attitude of almost deliberate rebellion on U.S. roads seems designed for chaos.
Its about having the right balance of rules. E.g. there should be rules about what side of the road to drive on, but maybe not about exactly how much room to give bikers (bike lanes).
Edit: I'm not suggesting that grocery stores create rules about how people walk around with carts...