Mat would have either been stuck defending Caemlyn while Moiraine rotted in Finnland until the Last Battle or Elayne would have destroyed the gateway (assuming the White Tower still knows how to do that) and the shadowspawn army would have gone to a different gateway and conquered much of Randland before anybody could stop it.

By balancing Mat's curiosity against his suspiciousness regarding AS Verin let his taveren nature decide how things went. It's basically a show of faith in the Pattern. For once we see a wot-character use taveren as it should be (as she did before with Perrin and Mat.) If she did as ya all suggest things wouldn't have been pretty.

I also have a suspicion that because in the new age there will be no Ogier, their marks on the world also need to fade away. Caemlyn and Tar Valon are foreign Ogierish monuments that don't belong in the new age of technological man. They have to be destroyed and rebuilt.