Ben W. answered 02/27/21
Classically Educated Business Analyst
Okay, so this question is a little more complicated than it sounds. I'm going to point you to a section of Aristotle's poetics because it's basically the cornerstone of classical dramatic writing. If you look at section 1.6 Aristotle lays out his definition of tragedy and what he sees as its core components. The basic idea is that tragedy is about serious action. Both of those words are important. We're imitating something serious about life, and that something has to be an action. You're welcome to disagree with him, but that's his argument.
He uses the rest of part 6 to talk about the important parts of a tragedy, Plot, Character, Diction, Thought, Spectacle, and Song, and which are most important. He argues that plot is the most important piece and that peripeteia ('reversal') is one of "most powerful elements of emotional interest in Tragedy" along with Recognition. Aristotle then keeps going down the rabbit trail of which other pieces are more important than the others.
The most important takeaway here is that, according to Aristotle's definition, you could write a tragedy without peripeteia, but it probably wouldn't be nearly as good as one with peripeteia. It's a very important, compelling piece to one of the most important parts of a tragedy (the plot), but that's all it is: a piece.
Hopefully this helps anyone seeing it - I do realize this is a really old question.