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.
Your response to the question is very perfect, would have said the same thing if I came across the question first, but all the same, he is not out of place asking here as well, maybe he thought it possible that some gambler here must have noticed and asked the same question in the past, and it was answered, so, possibly, he needed a re-answer to the question.
Personally, I've never played COIN-flip, but I've played dice multiple times way more than I can even number, I don't know the mechanics behind coin-flip but if it's exactly as I think it to be, then there should definitely be an Auto mode for it just as we have it for dice, I will definitely have to find out why as well.