Yes, milk can serve as a quick and easy post-workout snack for runners, however, it’s not entirely necessary for all runners to drink milk.
One 8-ounce (1 cup) glass of cows’ milk provides 8g of high-quality protein which is important after exercise because it promotes muscle synthesis [ 1
1]. Cow’s milk is rich in an amino acid called leucine, which is particularly effective for muscle-building. Pairing a glass of milk with a serving of fruit after a workout offers a balance of high-quality protein and carbohydrate to replenish glycogen stores and promote muscle synthesis.
Cow’s milk can also help runners strengthen their bones, and replete minerals lost through sweat such as calcium, magnesium, and potassium. Find more information on optimal nutrition for runners here
 James, L. J., Stevenson, E. J., Rumbold, P., & Hulston, C. J. (2019). Cow's milk as a post-exercise recovery drink: implications for performance and health. European journal of sport science, 19(1), 40–48. https://doi.org/10.1080/17461391.2018.1534989