ARM derivaties need less circuitry for the same computing task and, as a result, dissipate less power. This is one of the key reasons for their dominance in the battery-powered world of mobile devices. (The other is the customization and integration flexibility provided by the ARM ecosystem.)
If you want to understand why Intel’s x64 chips won’t ever show up in an iOS device, you have to recognize that ARM originally became dominant in mobile for one reason, and that it’s dominant in mobile right now for another reason entirely. I think it’s safe to say that Apple, along with the rest of the industry, originally chose ARM-based chips over Intel’s for JLG’s first reason — their longer battery life.
As time went on, however, and ARM became entrenched in the smartphone and tablet spaces, the architecture’s customizability (JLG’s second reason) became just as important to Apple as its low-power design. It allows the company to create everything in tandem — iPhone hardware, iPhone software, A-series chips. Even if Intel were to show Apple an x64 chip that consumed less power than Apple’s ARM-based chips, Apple wouldn’t switch. Battery life is important, but ARM’s customizability is what allows Apple to be Apple. The most important aspect of a mobile architecture to Apple today is its customizability — and x64 doesn’t offer any.