I think people of all classes have birthday parties for their young children. (Unless the parents are simply devoid of class). It need not be expensive. I remember having backyard birthday parties when I was very young, the most expensive thing being the Barney the Dinosaur character. I don't think Chuck E. Cheese or Laser Tag is that expensive either. (Unfortunately I don't think I ever had my own birthday party in either venue, although others' birthdays)
What is truly obscene are the "Sweet Sixteen" parties held for rich girls turning 16. I've heard of Wall Street bankers spending six figures on dream fantasy "Sweet Sixteen" parties for their daughters. "Sweet Sixteen" is something that needs to be abolished.
This, but I think sweet sixteen birthday parties are common across all classes.