In fairytale land that sentiment would flourish beautifully. Everyone would hold hands while fluffy unicorns and rainbows pop out of the woodwork.
As overly optimistic as your sentiment is, I don't disagree with it, but the city isn't a stage where that would be openly accepted. We're talking about centuries of ingrained differences between the gifted and ungifted. Suddenly uprooting that would be seen as an affront by many, and potentially cause more unrest within Haven than securing any peace outside of the walls.
Even if you managed to get a nongifted representative onto the council I highly doubt they'd be little more than a figurehead. They would still be outvoted on every turn for the benefit of those with powers, because that's the way the city works. Whether or not it should change is moot, because it simply won't. Those in power don't share power any more than they have to. The only way those people will get a true vote is for there to be an equal number of gifted and nongifted onto the board, and that's never going to happen. Sure, in a perfect world some representation is better than no representation, but that doesn't necessarily mean anything would change for the better.