I don’t think browser is an integral part of a device. Apple might actually run into some difficulties if it defines what is ‘integral’ too narrowly?

So why move Chrome to iOS? This is a preemptive move by Google. Currently Apple has absolute control over their app ecosystem, but that hinges on one thing the lack of competing web app market places. Currently Apple has been happy to play along with the browser improvements and is actively adding new features to their browsers, but they don’t really have any particular interest in doing so. They don’t derive any revenue from the browser usage, and as things are beginning to shift back toward web apps and emerging standards compete against native app features they are going to reach a crossroads very soon. Do they keep supporting innovative features in the browser that allow developers to parallel native features outside the app ecosystem?

Google has a significant interest in ensuring they maintain access to the cutting edge features of the emerging browser standards so they can leverage the browser as a gateway to their customers even on Apple’s platform. With the divide between Google and Apple growing, it makes since for Google to get their trojan horse into Apple’s cash cow before Apple’s priorities shift. For example Google could release Google Maps as a web app as soon as Apple releases their new mapping system.

So this move seems inevitable to me, Google has to do it, and hopefully if Apple prevents them from innovating in this space. Google can rely on regulatory pressure to ensure it happens because it is bad for consumers if Apple does not allow people to innovate in the browser space.

As to why chrome would be successful on iOS because it will be the fastest. Google will spare no resources in making Chrome for iOS the fastest they possibly can and will consistently add new web standards because this will become a significant source of revenue for them. Aside from that they can use Chrome as a platform across all computers and mobile devices to create a second tier of apps and services outside of the native platform environments.

Due to public and/or regulatory pressure? As you mentioned, they did not allow third-party browsers in the past, but they allow that now. I doubt that they voluntarily decided to allow third-party browsers out of the goodness of their heart. Similarly, there’s a good chance that they can be pressured to allow third-party browsers to be set as the default browser. After all, it’s the right thing to do.