Bereavement fares, with their full-Y flexibility (hence the cost), can make sense when you're going to visit someone who is very sick or on their death bed but you really don't know how long you're going to be there; e.g., how long before they're out of the hospital or how long before they actually die, how long before the funeral happens, how long before affairs are finished up. Even so, a cheap round trip plus change fees can still be cheaper, as djerikd mentions.

If you're travelling to a funeral where you already know the date, just get whatever cheapest roundtrip you can. Or use miles.