You don't have to use Unreal Engine, there are many others and you can write your own.
Distribution to apple devices requires using apple's store, which is really the core issue here. If IBM/Intel/MS could pull this off in the 80s we'd still live in a stone age.
You can achieve the result of making an FPS game without Unreal Engine.
You can't achieve the result of offering your product to about half US phone users without apple store.