I think traverse analogues to the map functions in Relude.Extra.Tuple would be useful:

traverseToFst :: Functor t => (a -> t b) -> a -> t (b, a)
traverseToFst f a = flip (,) a <$> f a

traverseToSnd ::  Functor t => (a -> t b) -> a -> t (a, b)
traverseToSnd f a = (,) a <$> f a

traverseBoth :: Applicative t => (a -> t b) -> (a, a) -> t (b, b)
traverseBoth f (a1, a2) = (,) <$> f a1 <*> f a2

(No analogue of dupe, at least for now, because there'd be ambiguity over whether it worked like \a -> join (,) <$> a or like \a -> (,) <$> a <*> a, and I'm not sure which would be better.)

The use case that inspired this was a function (FilePath -> IO (FilePath, String)) that takes a filename, and returns a pair of the name and the contents. With this proposal, such a function would simply be traverseToSnd readFile.

If this idea is acceptable, I'll make a PR that adds it along with hlint rules and tests.