The reason your city's status of Enthusiastic doesn't count is because the quests are not to "make the people happy", they are to add x amount of Happiness. This can be done easily if you have Faces of the Ancient and/or Gates of the Sun God decorations from GE. You just build and delete them until you've fulfilled the quest. All you need is a free 2x2 space in your city.Something that has to change in Events are the Quests that require making the People Happy.
My Population is always Enthusiastic but that never counts to the Quest, it should be an automatic completion.
I have to waste supplies and time etc. tearing down buildings that I need for Happiness buildings that I don't need just to take those down again after the Quest to replace with buildings that I had (more hours of production wasted). That is not fun, it is annoying. I have seen players giving up on Events, even leave the game, because Events can be a pointless pain with little reward.