I seem to recall asking for this feature some years ago and being told it wasn't going to happen, but it seems silly to me that if I suddenly realize I posted a stupid answer that can't be redeemed, I have to rush to open my web browser to delete it. So what is the reason for not allowing it?
There is no good reason for it other than limited development time and resources back when the apps were being actively developed. It is possible from the iOS app, so the API supports it. However, right now, all development on the apps has been frozen.
And there's no real reason to rush; you can always delete an answer. A single downvoted deleted answer won't cause much harm (unless you're posting a lot of bad answers and are at the risk of a low-quality answer ban).