I'm not sure that this is ever addressed in canon, but logically;
The Reavers may have proved useful to the Alliance.
It is well known that not all of the planets in Firefly and Serenity were happy to become part of the Alliance, with an army of "Browncoats" fighting for independence from the Alliance (and ultimately losing). The Alliance is made up of a series of "core planets", with planets further out classed as "outer planets" resembling the 19th-century American West and being generally less civilised than the core planets.
It was the outer planets that made up the bulk of the Browncoats, many of whom still detest the Alliance after the war was over (see: Malcolm Reynolds). Politically, these outer planets are officially under Alliance control - but they often have very little regard for the Alliance and their attempts to control them. Naturally, the Alliance would be aware that they are not popular in these areas, and have probably considered the possibility of another Browncoat uprising.
So from the Alliance's perspective, the Reavers prove to be a useful resource. It is the outer planets (those associated with the Browncoats) that are most often attacked by the Reavers, planets that are unable to defend themselves and as such rely on the Alliance for protection. This reliance means that the outer planets may believe it too dangerous to attempt to "secede" from the Alliance in another civil war, guaranteeing the Alliances continued control.
In conclusion, the Reavers pose nearly no threat to the Alliance, but help ensure the continued loyalty of the outer planets.
Edit: It has been bought up in the comments that the Alliance might deny the existence of the Reavers. Even if they do, I'm sure the outer planets (which are aware of the existence of Reavers) feel more secure under Alliance control, so the end result is the same.