Of course, it will require exponential data for zero shot. The keyword here is zero shot. If you think about it for a second, this applies to humans too. We also need exponential training data to do things without examples.
When we learn to drive, we do not need to crash our car a thousand times in a row before we start to get it.
When we play a new board game for the first time, we can do it fairly competently (though not as good as experienced players) just by reading and understanding the rules.