Sasha Putilin writes in the defense of em dash:
I fucking love em dashes. There is no greater joy in life than typing a sentence, realising it needs a clarification, a caveat, an addendum — but in the same sentence, not a new one — and, guess what, the em dash is right there for you. You want to package things neatly together — and the em dash lets you do exactly this. Em dashes make writing feel like you are assembling lego bricks.
Em dashes can be used instead of brackets in a sentence — like this one for example — and you can just type your shit and keep going. Brackets are for people who raise their hand in meetings and say: “this might be a stupid question”. A parenthetical is whispering: “Sorry, don’t mind me, I’ll be quick”. Em dash kicks the door open and announces itself. Use brackets when you are embarrassed by your own thought.
And also occasionally — occasionally — one just needs a random dramatic pause. Punctuation marks originally evolved as pause or breathing markers, after all. It’s not like grammar and punctuation rules were sent to us by god in their final form. People were just writing shit, and at some point the most popular patterns got codified. Sure, you need commas to signify a small break. Then em dash is a natural way to express a larger, longer, break. A period is great to express a complete thought — and it shifts the register of the next letter.