Simple as that - is there any reason to build upgrades on tiles that are more than 3 away from the city? Normal ones, not the ones with luxury/strategic.
One additional case where it's worth building improvements more than 3 tiles away is when you're playing as Polynesia.
You get +1 Culture per Moai, plus +1 Culture for each directly neighboring Moai. Moai outside your workable area still count as neighboring Moai.
So if you're building a lot of Moai, it's worth building Moai 4 tiles away, so that they'll add the neighbor bonus to the ones 3 tiles away that you can work.