While playing the game I've looked over a lot of neat details, the most prominent being item descriptions for every tower and every troop. This is interesting because every other game that has these also has a very large story/system of lore.
Upon reading through all that I've unlocked I've come across a substantial amount of information, almost enough to declare that someone at Supercell tried making a story behind the game. I looked at what seems to be a minor power struggle between the Ivory Tower Wizards and the Alchemists. I've looked at the Heroes and the effects of Dark Elixir on troops. I've even looked at how when you click on troop camps barbarians and archers will look up to you and wave as if they actually see you.
What I mean is that I think Supercell should try to incorporate a story into the game. Carefully, of course. There seems to be good potential and it would make the game a lot better for some people.
Here is just some things I've theorized based off of the current descriptions:
There is a power struggle over who is doing more for your base between the Ivory Tower Wizards and the Alchemists.
Alchemists make laboratory, Wizards respond with Spell Factory
Alchemists improve troops, Wizards respond by going into the fight themselves
Wizards build their towers for defenses, Alchemists begin working towards utilizing Dark Elixir
Wizards build Hidden Teslas, Alchemists respond with Inferno Towers.
I also see where a lot of work could be done with the Heroes and their relation to P.E.K.K.A., who is almost as strong as the Heroes but runs off of normal elixir and is aligned specifically to no army (i.e. "Is P.E.K.K.A. a knight? a robot? a samurai? Nobody knows!" )
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Another thing I would like to see is moral alignment. If you go and look at the top 100 players what will you see? Nothing but dark, sinister looking town halls and buildings. Going along with the lore request above I think there should be a way to change how all of that will look by the time you're maxed out. Perhaps by using too many troops from the dark barracks or utilizing too much dark elixir you can slowly become a more diabolical looking base, while using normal elixir and normal barracks keeps you looking pure and tidy.
Something else cool would be having replays for singleplayer maps (only on the victories, however.)
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Most importantly:
Honestly, I would spend more money on this game if there weren't micro-transactions. I know it's a pretty boring complaint and everything I've said prior to this will probably be trashed just because of this but it needs to be said. If this game would just cost money to buy and you took out all of the microtransactions and shortened the waiting times I would buy it. Seeing as how it's free and just has micro-transactions though I almost guarantee I'll never spend a penny on it. I really love it and it's amazing but micro-transactions are just the filthiest way to make money.