Well, yeah... nobody needs diamonds. That's part of the beauty of this game to me: the whole game is playable without spending. I've never purchased diamonds. Like Soggy, I prefer the challenge of figuring out how to make do with existing in-game resources.
But there's a difference between not needing diamonds and not using diamonds. They're just another game resource, and they do make many elements of the game easier or better.
Personally, I've used diamonds to buy some wiggle room in efficiency, both of space and time. I started this game to make a pretty city. Then realized that efficiency is key to a lot of things. I liked those things and I like the puzzle of efficiency, so my goals shifted. Now, with help from diamonds, I've shifted to a city that still lets me hit hard on the spire and tournament, but allows room for me to place buildings just because they're pretty, and waste road connections, and not worry so much about the per-square use of anything.
Most of my diamonds have gone to premium expansions. I've bought a few magic buildings, but do mostly rely on the spire to provide those now. I've also occasionally used diamonds as ultra-short timer instants, when I really can't wait for another 45s and don't even have the time to sort through my instant inventory.