It wouldn't be feasible to do this on iOS. It'd required everyone of their customers to jailbreak their phone, and then all of the app developers would violate the TOS with Apple by releasing the app in ways that circumvent the app store.

My brief reading of the iOS guidelines [0] says this is not allowed:

> 2.25 Apps that display Apps other than your own for purchase or promotion in a manner similar to or confusing with the App Store will be rejected

[0] https://developer.apple.com/app-store/review/guidelines/

Amazon's own OS is a fork of Android, and the Amazon Appstore consists almost entirely of Android apps you could also get through Google Play. So it makes sense they'd do it for just Android.

On Android, installing a random apk is as simple as

1. Allow installs from unknown sources 2. Download and install apk.

Can't do that on iOS without jailbreaking.

Closed system. There isn't a good way of doing this on iOS that isn't complicated. Too complicated for the average user.

iOS doesn't allow apps to be installed outside a few apple controlled processes without a JailBreak.

I don't think Amazon would want to launch a product dependent on JailBreaking. Unless Apple is forced to provide an API for alternative app stores, I can't see this ever being allowed. Unless of course apple rips off the idea and does it themselves.

Could Apple take legal action if Amazon were to try that? (hypothetically of course)

My understanding is not directly, however it could be argued that they were encouraging the end user to break the EULA on the product and thus interfering in the contract between apple and the end user. Different legal systems would view it differently.

On the other hand, apple could just throw more money into securing the phones from jailbreaking and end the business model much easier.

Because it's a pain in the ass to sideload apps on iOS.