I know at least Google and HTC directly support allowing you to unlock the bootloader (part of rooting), I don't know about others.
Unlock the boot loader would void your warranty.
Samsung also have their Odin application floating around internet...Odin would allow you unlock the boot loader, root and eventually install ROM
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Except you don't own the software you license it from Apple and their terms and conditions state that they can make future updates at their discretion.
https://www.apple.com/legal/sla/docs/ios6.pdf
So iOS 7 capable device owners can stay on iOS 6 but I don't see anywhere where Apple would be legally required to support it.
They don't... It is perfect legal for Apple to drop support iOS 6... In turn Apple is suppose make sure iOS 6 at least functional. Apple can do whatever they want, but not buy cutting essential features... It is just not ethical way to do business... But it is perfectly legal...