All right, sometimes writers pull it off -- Bird Boy manages to open with a (brief) mythic legend and catch interest with it -- but not often. As with sagacity, it is a wonderful chance to show off the depths of your shallowness. Myths need to be profound. They also need a mythic style to convince. (Are all myths profound and told in a mythic style? Of course not. But fiction writers must face that unlike real myth-makers, their myths need to be convincingly mythic.)
You can put it in someone's mouth to temper it. Which will also make it more dubious, which can be a plus or a minus.
Another thing to watch for is basing on it some theory of the religions and going to construct your own on that principle. The problem is that, besides the skeleton usually being too evident, is that the theory is seldom as all-encompassing as it claims. The solar-myth theory of stories was once used to explain a whole heck of a lot of them. Even modern day explanations, resounding with the spirit of the age, aren't going to sound convincing to a lot of people.
And, of course, a lot of people go for creation myths. Creation myths are greatly overrated because while the logical order for a book of myths is to start with them, nevertheless this overstates their importance in the set of them. Plus, of course, as C. S. Lewis observed, most of them explain how the world started rather like explaining how Hamlet started with the ghost on the ramparts, but in many fictional versions, under the influence of Genesis, explain it with Shakespeare -- without realizing that that will drag in a lot more into the world-building to be convincing.