I have a question: Why does the Dice game have an Auto mode, but the Coin Flip game doesn't?
This is a question you should have asked the live support team and not a forum member - they are the only one that can provide you with the answer to this question not someone that doesn’t have any inside information.
Try asking them via support and see if you can get an answer from them.
The answer is simple, because the game is totally different than dice.
At coin flip you chose a side and after the flip must decide if you cash out or do another flip. Dice does not have this cash out feature and the round is finished after the "throw".