There are some other things that stay in the 'ready' state unless you hit the button twice or lock the car. The best thing to do it hit it twice OR lock the car when exiting to ensure as much as can be goes off as soon as possible. In the big scheme of things, I don't think it really makes all that much difference, though, but I do the double-tap most of the time.
My other BMW operates exactly the same way, and there are times when I may like to sit there and listen to the radio prior to leaving, so it doesn't bother me. Note, you can cause the radio to turn on for about that same 10-minutes when entering the car by pressing the radio button without hitting the start button (which will wake up other things as well).