At the end of the day, the Typhon Pact isn't built on what makes the Federation strong. They're all individual empires of opportunists. Their cooperation will be short-lived; a few years, perhaps a decades worth of story time. Eventually, one race will depart and not long after it'll splinter. Hate is not a strong enough binding force, thankfully. They may win some battles, but they'll lose the proverbial war.
That said it's a good story device and I like it. I even had the same idea years ago in my own thoughts - of a bunch of "evil empires" banding together as an anti-Federation. I'm sure many of us have thought of such at one time or another. I'm surprised it didn't happen on-screen, TBH.