In a combat aircraft the advantages for getting rid of the pilot are numerous: less weight & volume for the pilot and their associated support kit, eliminating the pilot allows for plane geometries that are just not possible with a human onboard, eliminating the pilot enables maneuvers that would turn a pilot to jelly, etc. The pilot is probably the most expensive component of a combat aircraft. Eliminating the pilot opens up new mission profiles (e.g. you don't have to worry too much about the aircraft getting back to base.)
For a commercial aircraft the benefits of going unmanned are not as pronounced and in some cases are non-existent. In addition to the lack of benefits, you introduce additional costs related to liability (you can always blame pilot error for a problem, but if there is no pilot then it is the airlines fault for either not maintaining the system properly or for selecting the system in the first place) and the fact that passengers are not going to trust this system anytime soon.
The impediments are almost completely social, but the benefits are so slight that it does not make much sense to bother aiming for completely unmanned. What you are going to see (and in fact what has been happening for years now) is the increasing automation of cockpit tasks. There will always be a human being "at the controls" for the forseeable future, but what that actually means and how much active control they are exercising is going to be slowly changing.