Chromecast and chromecast built in do not have the same functionality if voice is a big concern then get a chromecast. Also the features you ask about are hardware dependent so it has more to do with your a/v setup than just the chromecast.

Google Home Hub is one thing and Mi Box S is something else. One doesn't cancel the other. Not sure if I misunderstood your question.

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If you have commands added in your Google account, they'll work no matter what device you use, provided that it has Google Assistant built in. My commands work on my phone once I set up my Google account. It's the same if I add a Google Home, or a Home mini, or an Nvidia Shield TV. Any device that has the Assistant built in will have access to the commands stored in your Google account.

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One more thing. Chromecast has nothing to do with Google Assistant. It's a different feature.