Coming from an EU West player:
-What are your impressions of the balance on Dominion? (If you're a serious player that's gearing up for competitive Dominion, I especially want to hear from you!)
I think champion balance is massively better than people are giving it credit for. I don't think there are any truly worthless champions nor any truly dominant ones. Many of the Stomp-effects occur due to the lack of coordination and coherence, and efficient counterpicking in a random solo queue team.
That said, I'd pick Kassadin for the strongest champion in the map; when played well, he can truly carry Dominion, something you can say for few other champions. Though this is also in part due to people not playing enough champions with hard CC on the map. Still, low cooldown blink is amazing as is packing multiple CC effects and some powerful AOE. I don't think he necessarily needs a nerf though; he's much more manageable in arranged teams (though his weakness in laning is obviously a non-issue on Dominion). Shaco is another champion with a similar kit and similar capability, though he underperforms quite often since most people play him AP, and his AD build is quite hard mechanically, much like Kassadin.
Overall, mobile champions with weak laning but strong scaling like Poppy, Blitzcrank, Kassadin and Shaco tend to perform above par on the map, alongside select few others. But again, I haven't found any of them truly problematic enough as to skew win percentages heavily in any way.
-What is your biggest pet peeve about Dominion?
Inane quests. Like when the enemy mid becomes a quest target for them because we happened to succeed a ninja capture. How are we supposed to defend it while capturing e.g. Windmill? Yeah, that's autoloss of the quest.
Windmill being quest target is another issue, as it's the natural target for attack anyways; it rewards one team for doing what they'd do regardless while forces the other team to do something super-risky. Enemy mid vs. Ally mid would be more fair than Windmill vs. enemy mid. Then both teams would be forced to do something risky to get it.
Point system is another one, but it's a minor thing since it is something I can just ignore. It's no worse than KDA on SR.
EDIT: Oh! Items. More specifically, Sanguine Blade (which pales in comparison to The Bloodthirster; needs to be brought closer to a full BT in power or need an alternative for AD casters), Odyn's Veil (which does not work on squishies, unlike Banshee's Veil it's replacing), Priscilla's Blessing (useless; since this map makes health regen irrelevant, it has no stats beyond speed boost), Prospector's Blade (c'mon, give it more Lifesteal so it's useful even without laning) & Oracle's Extract (without Vision Wards, this is the only non-slot way of dealing with stealth and with how easy it is to force a kill on someone on the map, it's very easy to remove; needs to be cheaper or have a cheaper alternative).
-Are there any players out there who now play exclusively Dominion?
Currently yes, though once I get my 2-to-1 win/loss ratio, I'll go back to ranked solo queue. 30+ min queue on a consistent basis is vexing, especially since some of the games are completely worthless. Queuing 30 mins to lose a non-contest to DC + having both, Backdoor Janna & Backdoor Shaco on your team is not very rewarding. This happens rarely enough and even out in the long run, but the queue times really amplify the vexing effect; when I queue twice longer for a game than what the game actually lasts, I kinda need the game to be of decent quality for me to find that a reasonable way to spend my time.
Of course, the only way to solve this is to get more, and better players for Dominion so I guess just marketing it more and arranging Dominion tournaments and Ranked Queues would be the way to go. Just don't let it fall the way of Twisted Treelines; push the format to get more players into it, and especially reward people for learning the map so there'd be a broader top level. Something that'd make it worth their while for Platinum-level SR players to play Dominion instead of Ranked Solo Queue. Maybe have teams play mixes of Dominion and SR in tournaments or something; something that forces good players onto the map.