That there are several real male and female characters in The Big Sick is a tribute to its writers, the real life couple whose story is presented in the film. There are very few caricatures in the film. The ones that might qualify are so deftly handled, it just feels like a person we know and not a punchline waiting around to be had.
Let's be serious though. This isn't mensa material. It's a big dumb action comedy. There is nothing here as funny as Thurber's Terry Tate, Office Linebacker and thank goodness there is nothing nearly as bad as We're The Millers. It might get a few sequels, and that's fine. I'm pretty sure I won't remember one joke in 5 years, but I will smile when I think about it, just the same.