> I should be able to install whatever app I want, without having to jailbreak my phone and deal with warranty nonsense from the manufacturer. Just like my computer, which I can also install whatever software I want on it.

I'm not familiar with Apple, but where do you see this problem in Android? "Allow installation of apps from unknown sources" is a one-button toggle in Settings, after which you can download an apk from anywhere you want and install it without issues.