I live in the Romanian countryside. Everyone here pasteurizes milk in a pan on the stove. No one goes through a quick cooling process: people just don't have conditions to do it, I guess. Instead, the milk is cooled in the pan and then poured into bottles and stored in the fridge. What is the point of the quick cooling that I read about on the internet?
It is safer and helps increase the shelf life of the milk.
Otherwise the milk will pass through dangerous temperatures and and may be recolonized with air born pathogens. These will grow rapidly during the period the milk is warm, and more slowly once it is refrigerated. While the milk may not become immediately unsafe or unpalatable, its storage lifetime will certainly be reduced.