Well, I'm the one who triggered the no-open-borders discussion, so here goes the history...
I decided to experiment with turning Open Borders off - completely! in order to increase AI tensions and cause more wars as my primary reason. "Our Open Borders Agreement Brings Us +1" seemed unnecessary. Also, the minor annoyances of seeing the Spanish attack me in China by land, or French and Roman cities in the Ukraine seemed to make it worth trying.
Not only did it work, it worked quite nicely. Europe looked more European. Germany and Russia were at each other's throats. The Mongols invaded India, which still might have been a complete fluke.
Then, when I started PLAYING instead of watching, as Rome, it added the strategic considerations of getting to the Atlantic much more pressing. Try to get Kopenhagen? Take out France? Northern Spain? Build a route through Africa?
I didn't even notice that I wasn't getting trade from cities that weren't my own, but then, I'm not much of a micromanager. So I came back and reported that not only was Open Borders kind of historically innaccurate, getting rid of it also helped the game.
I agree with the idea that trade should exist automatically when relations are high enough, however, some leaders (Izzy, Monty, Tokugawa, Genghis) always seem to be grumpy, and this might cripple them further.
I would save Open Borders (as an effect) for Defensive Pacts, Permanent Alliances, and maybe mutual wars with allies with high relations. I think what I would do is make Defensive Pacts appear slightly earlier, include Open Borders, and require a slightly higher friendship level to sign.
Just curious - has anyone else actually played with Open Borders switched off?