iTunes won’t play on iPhone 13 in carplay

Had the same issue. For those still experiencing the same, I finally fixed it by Resetting Phone.

Go to the “Settings” app > Tap “General” > Find and open tap “Transfer or Reset iPhone”> Tap “Reset” > Lastly tap on “Reset All Settings” > For security reasons, you will be asked to enter the iPhone Passcode. 

Me too I have seen many discussion forums of people saying playing music through Apple CarPlay crashes it with iPhone 13 seems to be a widespread bug

Mine won’t play either it’s annoying they said it’s a known issue they’re working on when I called support but omg it’s annoying

That's what I did and it fixed it too.

Hello,

‘’I have learned two Options.

‘’The First Option, Using your phone - Go to settings > music > EQ and turn on a choice of music, Play a song for about a minute but not on CarPlay—-on your phone. Then go back to settings > music > EQ and turn the EQ off. Plug your phone on and it should work.

If not your second Option. Is to reset back to factory settings. See if that will restore your phone go to settings and then General tap reset and and reset. all settings. Follow prompts.

I hope this helps, I just learned it and I hope I have given you the correct information