The TLDR; answer to all your problems is: "Just use a freaking USB cable".
I rent tons of cars and my experience with the wired AndroidAuto is:
1. Plug it in.
2. That's it. It just works. No ToS or any other crap.
3. The same cable also supplies power!
Some cars _may_ need me to press something on the screen to switch to AA mode, but it's rare.
And it works perfectly with _everything_ on my phone. A navigator properly pauses my audiobook before announcing a turn, for example.
for rental it honestly probably make sense, since this is not your car.
Why on earth everytime i sit in the car i have to neurotically plug the cable. I had situations i forgot and in the middle of the ride i started to look for cable or try to wire car play, simply because i figure out i don't know where to go .
This type of crap is not convenient and simply dangerous.
what proper car should offer: keyless enter; keyless profile adjustment including seats, heat, music profiles, etc wheel etc; keyless start and go;
one of the best tiny features i have. In the morning i drive to work; i can go several ways there depends on traffic, My car knows that in the morning i go to work; GPS is on, traffic is calculated.
I open the door , my music started to play, I press gas and drive; zero cables, zero pairing ; open the door and drive.