What if China told everyone in the world, "Stay out of the Pacific Ocean, or there will be war.", or what if India said, "Don't sail the Indian Ocean, it's ours, so if you enter it we will go to war!". Would it be realistic and acceptable for the rest of the world to just stop sailing in the Pacific and/or Indian Oceans based on a threat like that? Because that's what the Dominion did. The wormhole didn't open up in orbit of their capital, you know. It took over a year before the Alpha Quadrant powers even directly encountered the Dominion. For the Dominion to claim the entire
Gamma Quadrant is just as unreasonable and unrealistic.