I think the idea was to have Demandred face all versions of Rand-lite. Gawyn is the least of them, the jealous brother in law who Egwene got stuck with after she and Rand ended things. Then we got Rand's step-brother. Then we got Rand's father figure and teacher. Tam would have worked well here too, but his character had far less build up, so it wouldn't have been as emotionally satisfying.

Another avenue would have been to follow up Logain's battle with Demandred with Egwene, and have her do the anti-balefire thing against him. Both Logain and Egwene are leaders who accepted (somewhat, in Logain's case) that they were a step behind Rand, something Demandred never could. Tied in with the whole Seal basketball they were playing, it would have worked (and Logain could have offed Taim, then).

Mat fighting Demandred would have been the least thematically satisfying, but it would have been a lot of fun. As it is, though, I'm happy that all Demandred got of Mat was what he thought was battle tactics too refined for anyone of this age. He was puzzled and totally blinded. And that was Mat's victory.