I'll tell you a story about my first time with an Android device.
I went to the store to download an app. And it failed.
Over. And over. And over again. The device emitted a cryptic error message which, thankfully, was easily Googled. The troubleshooting steps required diving into the settings application and manipulating some controls to reset a data store in a low-level component in Android's OS.
Contrast that with an iPhone, which just works.
Apple's value, is, and shall remain, their airtight integration and reliable user experience. Putting Chrome on there touches none of that. None of my non-technical friends or family will ever touch it.
It's healthy for Apple to let third parties write whatever apps they want, so long as those apps don't impact system stability or security. Apple's industrial design makes hardware that's very difficult to successfully imitate, their content ecosystem is complete and richly integrated into their products. Their software and hardware are built in tandem.
No one is positioned to handle the whole enchilada as they are. When that changes, that will be the moment to worry. Meanwhile, they're in good shape.