During the 1980s, there were several ugly, or at least, embarrassing incidents involving Delta Force. The item that got the most attention was the accusation that Delta Force members had embezzled half a million dollars in money meant for secret ("black ops") operations. Exactly what was going on in several different incidents is still somewhat murky. It appears that Delta Force, and a special unit of SEALs, was seen by the CIA and the White House as an adequate substitute for the secret activities Congress forced the CIA to abandon in the late 1970s. This was also the era of clandestine, and often illegal, U.S. operations in Central America and the Middle East.
Delta Force and the Seals survived this, but perhaps as an after effect, Delta and Seal Team Six were both placed under the control of the Joint Special Operations Command (JSOC). Despite that, the use of Delta Force and SEALs for CIA and other intelligence operations continues. This makes sense, as a string of embarrassing incidents and lots of bad press caused the CIA to shut down much of its overseas agent operations. But there were still situations overseas, often unanticipated ones, where you really, really needed to get an American in there to look around or make contact with local agents. Special Forces and JSOC operators were just the thing. While many of these guys look like pro football players (kinda makes them stand out, even in civilian clothes), many do not. Turning one of these guys into a secret agent is apparently not difficult. And they already have a license to kill.
One thing that may make Delta more likely to be used in the future is the availability of better intelligence capabilities. Some of this is new gadgets (drones and information analyzing software), but a lot of it is a new willingness to put people on the ground (CIA or Special Forces) to collect information Delta needs before they can plan and execute a successful mission. And often it is Delta that is going in first to ferret out the information needed to prepare an armed strike.
No one has said much, officially, about the use of American commandos as spies and intelligence agents. But these lads are trained to be flexible, think fast, and operate under any conditions. While they normally train wearing camouflage uniform and carrying an assault rifle, they have no problem going on a recon mission in a suit, armed with a 9mm pistol, or no weapon at all.
Delta continues to learn from British SAS, who have long made good use of close working relationships with British diplomats. In this respect, Delta may begin performing secret operations (that stay secret) involving anti-terrorism activities or nastier forms of diplomacy. If the word was ever given to kill Saddam Hussein, Delta would be the designated executioners.