I find myself somewhat on the fence about this proposal.
Ultimately, I'd like to see semigroups in base.
That said doing so with the current changes in flight is somewhat awkward, and introducing it carries a lot of distributed work.
We have two outstanding proposals that have received overwhelming support: namely the Applicative => Monad (AMP) proposal and the generalization of the types in the Prelude for mapM, etc. to use Foldable and Traversable (FT). Between these two proposals, we wind up with the need to bring in Foldable, Traversable, Applicative and Monoid into the Prelude. Applicative as a superclass of Monad and for traverse and Monoid because Foldable brings in foldMap.
Consequently fixing the situation to make Semigroup a superclass of Monoid isn't something that can be done purely by adding a module to base, but it would infect Prelude.
This makes it have to clear a much higher bar!
A real proposal that involved adding Semigroup as a superclass of Monoid could possibly be concocted like David's AMP patch, whereupon Monoid would be given a default mappend = (<>)
That could enable users to just have to write an extra instance line like they would for the AMP, but it has some immediate headaches.
In particular (<>) has been in use in pretty printing libraries since time immemorial. Suddenly exporting a version from the Prelude is likely to be a fairly breaking change to those libraries as the associativity of the (<>) provided by Data.Monoid (and the one provided by Data.Semigroup) both disagree with the (<>) in Text.PrettyPrint.HughesPJ, which is in the platform already. This could lead to some rather annoying breakages -- worse, silent breakages. I seem to recall that there was some concern that this would change the output of some pretty printing in GHC when the associativity issue was last raised on this list over the introduction of (<>).
I think to have a serious proposal that could actually be accepted, a lot of work would have to be put into a patch and then it would need to be explored how much the associativity issue bites users in practice along with gauging the amount of effort that would be involved in retrofitting semigroup instances into virtually everyone's libraries.
My knee jerk reaction is to try to put this off until the dust has settled from the AMP and FT changes and push back with a request for the necessary analysis.