I'm not familiar with Teslas at all, but it sounds like a voice interface might help work around some of these limitations, a la Alexa/Hey Google. Maybe they already have it?
They do. You can control many things with voice in Tesla.
I don't know the comprehensive list of things you can use it for, but so far I used it to:
* Change temperature
* Play a specific song
* Set navigation to a new destination
I didn't put switching music tracks (next&previous)/adjusting volume on that list, because those can be easily performed using the scrollable button on the steering wheel.
It's like playing an old text adventure without the manual, so you don't know the verbs. It uses too much thinking to try to come up with different words while also trying to drive.