Yes, but there are also a lot of times where they don't in my personal experience. If there's a question about who technically got there first - like two cars approach at roughly the same time - the rules aren't always followed as written by other drivers.

First to stop is the safer option. I feel that most people around here follow that too.

It also has a rare benefit of seeing the interaction between a majority first-to-goers at a 4 way.

Not in my experience. Of course, as long as people are actually stopping, someone already stopped has an advantage. But that's a difference between East and West Coast US driving. In the East people come to a complete stop before moving again. In the West they'll slow down a lot, nearly stop even. So there's definitely regional characteristics. But the most common law is that of our childhood, possession is 9/10ths of the law.