He doesn't operate heavy machinery either. Spouses of political leaders don't have much responsibility either (they can insert themselves into political situations but at the end of the day, they are not accountable to the voters since they were never elected).
Those in an appointed/elected area of responsibility need to be capable of doing their job while in that position. Rush is just a commentator/entertainer. He holds no elected office and carries no authority. His listeners listen because they find him informative some of the time but his audience does not come to their facts simply through him. They have other sources. They call in/listen to his show to hear his views on news in and outside of the mainstream media.
If candidates and even Clear Channel decide to stay away from Rush Limbaugh, that is their decision to make. Rush's radio show does not seem to have suffered in its' production or performance as a result of his addiction (even his hearing loss which some attribute to drug abuse did not significantly lessen his radio show).
JFK getting injections of pain killers so that he could sit at a table and negotiate with the head of the Soviet Union put American safety at risk. This is not drug abuse but then again the President will not be at the top of his "game".