Libertarianism secretly relies on most individuals being prosocial enough to tip at a restaurant they won't ever visit again.

I'm puzzled that you gave that specific example, given that it's obviously wrong. Most countries do not have a culture of tipping, and their economies don't implode. They just have less headaches at bill time. And in many cases (a long way from libertarianism) their wait staff get paid a living wage.

I'm also not sure what it means for libertarianism to rely on something, since libertarianism is not an actual functioning thing in existence. But if it did exist and function, it would not rely on tipping.