From an ATC viewpoint, normally there would be no restriction if other air traffic wasn't a factor, or danger/restricted (etc) areas, and the pilot was prepared to maintain his own terrain clearance visually - which would normally be the case in a sightseeing diversion.
These days, such requests hardly ever happen in the world of airline flying, in my experience. The airlines themselves are quite keen that flight crews do not use more fuel than the flight requires. On-board monitoring on a lot of aircraft will ensure that the airline operations people will see if something unusual is occurring.