It still seems kind of silly, though, how they left their side of the wormhole so lightly defended, even when they knew how aggressive Dominion was being.
The AQ terminus of the wormhole was far more highly defended than the GQ terminus, considering the far side of the wormhole opened up nowhere near Dominion space. Remember, it took a couple years for the Dominion to really notice the AQ traffic entering their neighborhood. It wasn't like the wormhole opened up in their backyard. The Dominion had no reason to bar traffic through the wormhole, since it wasn't in their territory.
Again, telling the Federation to stay on their side of the wormhole and out of the GQ would be like China telling the US to stay out of the Pacific - an unrealistic and unreasonable request meant to provoke and provide a cause for hostilities.
There is no such thing as a perfect situation in life.
By traversing the Gamma Quadrant, the Dominion simply got madder and madder. Look, not everybody is rational, and not everybody even holds the same concept of rationality. The Dominion detested solids, and to them
annihilating any solid in their domain/sphere of influence is rational.
Besides, to use your China example, I think not going to the Yellow Sea or Sea of China in a state of cold war makes absolute sense.