I got to be honest, I hate when people throw out the word "stereotyping" like it's automatically a bad thing.
Stereotyping is a technique. It's a shorthand. Especially in a really short piece of fiction, you don't have room to fully explore a character, show the depths of their psyche and how they came to be the way they are. And often that's not the point of the story. So you paint with broad strokes instead of tiny ones. "You all know THIS guy, amiright?"
Especially when it comes to satire, which is where this story falls. You HAVE to establish the stereotype in order to subvert it. That's what makes the humor relatable: "I totally know that person!" That's what makes the humor, period: "This thing you were expecting? Turns out it's the opposite of that! Expectations thwarted!" That's what provides the character growth at the end and makes the ending satisfying: "Hey, she's not just a stereotype after all, there's a real person in there".
When done badly, stereotyping is just lazy writing. By all means, criticize bad writing all day. But using stereotypes does not *necessarily* mean lazy writing has taken place; sometimes the author choose to use that tool, just like the author might choose to show instead of tell, or any of the other million things you're not "supposed" to do.