your playing/building veigar wrong, he is pretty good in dominion. Ashe is decent, certainly not the worst. I have yet to see a Taric carry a game to victory however.
Veigar is one of my mains, and I can safely say he's a bottom 5 champ in Dominion. He doesn't farm very efficiently, and he's forced into suboptimal build options due to the fact he gets raped by long cooldowns as well as a complete lack of real damage output. The only way Veigar wins in Dominion is if the other team feeds him champion kills, and one thing that hurts him a lot is he's actually not guaranteed to be able to counter another ranged AP nuker due to them not being as common options in the Dominion meta. So a lot of the time, when you pick Veigar, the game is a 4v5. When I get tired of pubstomping Dominion with actual good champions like Garen and Karthus, I take Veigar just for a challenge since I'm better than the majority of most of the randoms I meet in Dominion.
Ashe is mid tierish. She farms alright and her ultimate is utterly insane on this map and her E is actually extremely useful in a metagame that lacks wards. Plus once she hits carry status, she wrecks stuff like a ranged AD carry should.
As for the worst champion in Dominion, I'd say Nunu personally. He doesn't farm well, he has no ability canceling CC, he doesn't kill people fast without his ult, and his ult is actually pretty bad given how easily it's interrupted as well as having a ridiculously long cooldown.