In that sense, really, what use would having the Typhon Pact be anything other than antagonists to the Federation/Klingons be? Surely there is no point in going in this direction unless the newly created entity opposes the established ones?
Here's the thing: It's true that drama requires conflict, but it's oversimplistic to assume that conflict always means fighting. Conflict means that the characters face an obstacle to achieving their goals, or are torn between conflicting needs.
Think about the situation I described within the Pact. Six powers, many of them prone to be contentious, trying to wrestle out a new status quo with each other and with the quadrant as a whole. That's a very volatile, potentially hazardous situation even if there's no immediate threat from those powers. Just being on the sidelines of such a dynamic can be a prickly place to be, and even if they aren't simplistically "enemies," there's the possibility that you could screw things up and make them your enemies if you handle the situation badly.
Not every Trek story is about fighting an enemy. Many of them are about facing a hazardous situation and trying to keep it from getting out of control. Many of them are about preserving the peace, trying to keep other powers from going to war with each other or succumbing to internal chaos.
And those new challenges arent going to come if the new political entity doesnt "oppose" the Federation.
That's not true at all. Maybe the challenge could lie in helping the Pact find a stable equilibrium that would be good for the quadrant and resisting those factions within the Pact that might tear it apart and prolong the chaos -- with the added challenge of convincing a suspicious Pact leadership that the UFP isn't the enemy. (I don't know if that's going to be the story, mind you, but it shows there are challenges other than straightforward opposition.)
There are plenty of challenges in politics other than open enmity. Just look around you at the real world. Study the relations that countries have with each other, and you'll find many complex and challenging situations that don't involve war or open hostility.
So what do you do if they are nice and peaceful with the Federation? What conflict does that create in the story?
You're making the mistake of assuming that the Pact's nature is already settled, or will be settled soon. As Allyn said, we're only at the beginning of the process. It could be years, even decades, before we know for sure whether the Pact will be a friend or a foe -- before even the Pact itself knows what its identity will be. Right now, they're still going through their birth pangs, and it's a turbulent and unpredictable time. That's where the danger, the challenge, and the interest lie. It's not that they're "the enemy," it's that they could be anything, that there are countless ways things could go wrong.
And it's not even just about the Pact. The whole astropolitical order in the Alpha and Beta Quadrants has been disrupted hugely by the Borg invasion and the Dominion War before it. What used to be relatively stable is now much more unsettled and turbulent, and that creates all kinds of challenges and risks. The Typhon Pact situation is merely one aspect of that. There are so very many stories to be told here beyond just another hackneyed "Us vs. Them" narrative.