They are only worth doing if you like how they look (such as the glowing effects).

They are only the "best" weapon for a brief period at the tail end of an expansion. As the previous poster said, there is a separate relic weapon grind for each expansion (aka each 10 levels from level 50 onwards). It's not worth doing during an expansion because crafted, extreme, tomestone, savage and ultimate weapons are better unless it's for an alt class that you don't play as much or you don't do raids. Once the expansion is over, it's no longer useful for stats and the reason to do it is for how it looks.