But at the scale of a national grid it's basically impossible to ensure that the entire grid is isolated from the ground all the time. Stuff breaks. And if the network is grounded in some far away place but not anywhere near you you get exactly the effect you describe: you have some unknown and potentially large voltage differential towards ground because the literal ground doesn't have the same potential everywhere. So instead you give up and tie one of the potentials to ground, and do that as often as viable.
However if you set things up so that one terminal of a 9v battery is grounded, and you lick the other terminal (just one), you would feel something.
(You would also have to be grounded, at 9v that would probably require barefoot on slightly wet ground. At 120v it's a lot easier to be grounded, but the principle is the same - you only feel the electricity because the ground itself provides a return path.)