I am puzzled. Maybe it depends upon the phone. I use a 1st gen Moto X (released in 2013, so fairly old) and I find cell phone integration on Model S awesome. When I walk into the car, cell phone connects automatically. Now if I want to play music on the phone, I switch to my phone as input on the media player on the big screen. My phone launches music player on it automatically and I can not only play/FWD/REV from the big screen and steering wheel buttons, I even get all the artist/album/song information on the big screen along with album art. This works for music stored on the phone or music streamed from google music, amazon prime or pandora. I have to touch the phone only if I want to switch the music source.
Any incoming calls are of course announced and I can take the call without ever touching the phone. If a text message comes in, any music playing is paused and not only the sender is announced on the car speakers, it even reads out the text message. I can then reply to the message just by speaking, no need to touch the phone.
I can also touch the microphone in google search bar on the phone to initiate any voice search which automatically pauses/mutes any music playing (even slacker or FM radio). It then records using car microphone. I can ask questions like how long will it take to drive to the airport, or what is the weather like tomorrow and the answer is read out on the car speakers. After that it goes back to playing music. I have to touch the phone initially to initiate this and after that it is all voice driven.
IMO cell phone integration in Model S is awesome. Just a different experience than yours.