Yes. If you have an electrical network that isn't grounded anywhere you can't get a shock from touching only one wire because there wouldn't be any current flow. If you repair electronics you might do that to a single device with an isolating transformer, or if you are a hospital you might do that to the entire building.
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.
For AA batteries that's true. But licking a 9V battery gives you a notable shock. Any wet skin should work to some degree at 9V, but the tongue is very sensitive so it brings the most dramatic effect.
If you lick just one, you feel nothing. You have to lick both.
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.)
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.