Well who else is going to do it? The intelligence agencies are the ones with all of the connections and experience with doing things secretly. Also, it is better to take out our enemies by deposing their leadership than by fighting an invasion to achieve the same goal. Spy agencies really offer great bang for the buck and can sometimes pull off regime changes without anyone getting hurt at all, even the leader being deposed.
Britain used to have MI numbers 1 through 19, now only 5 and 6 exist. MI9 used to aid resistance movements and aid escapees, MI19 used to interrogate enemy PoWs, MI14 was responsible for Germany and German occupied territories.
The CIA could hand intel to specialised wet work agencies, rather than acting on their own intel and therefore skewing the take and having the tail wag the dog.