If you can use a hot-word, what's wrong with using voice recognition to achieve what you want to do anyway? Using voice takes less effort.
Absolutely, you can use the same utterances to invoke the same intents in a car from a home setting.
"Alexa, set temperature to <x> degrees"
"Alexa, set volume to <x> or increase/decrease volume"
The first one seems more troublesome. This is less intuitive than touch screen based interface. The only way I see fighting against this is to standardize a set of generic gestures, map onto existing equivalent touch/voice actions and push it to the Android ecosystem. But not sure how many third party manufacturers will join this parade. Does this technology work well under screen? The industry is now obsessed with getting rid of notch and if Soli blocks this path then it will be a pretty hopeless fight.