As far as I can tell, there is no possible operation that one can perform today that requires the privileges of a U.S. single-engine ATP.
The ATP is required in Part 121 operations, and in certain Part 135 and Part 91(k) operations. Part 121 prohibits the use of single-engine aircraft (14 C.F.R. 121.159). Part 135 requires an ATP only for the PIC of (1) turbojet airplanes, (2) airplanes with 10 passenger seats or more, (3) multi-engine airplanes in commuter operation, or (4) helicopters. (14 C.F.R. 135.243(a)). Part 91(k) requires an ATP only for the PIC of multiengine turbine-powered fixed-wing and powered-lift aircraft. (14 C.F.R. 91.1053(a)(2)).
So, the only way you would need a single-engine ATP is if you were flying Part 135 in a turbojet or an airplane with 10 passenger seats or more. But, to be flying in Part 135, the aircraft needs a standard airworthiness certificate. Aircraft with special airworthiness certificates can't be used to carry persons or property for compensation or hire. (14 C.F.R. 91.313 - 91.327). Transport and commuter category aircraft must have at least two engines. (E.g., 14 C.F.R. 23.3(d)). Normal, utility, and acrobatic category aircraft can have at most 9 passenger seats. (14 C.F.R. 23.3(a)-(c)).
So, unless there is some screwy old airplane that has a standard airworthiness certificate but has more seats than allowed under Part 23, the only operation that would require an ATP is a Part 135 operation using a single-engine turbojet with a standard airworthiness certificate. I don't believe that any such jets currently exist.
That will change, once the Cirrus SF50 is certified. No idea if the FAA will allow them to be used in Part 135 operations, but I can't see why not. Then you all can dust off your ASEL ATP certificates and actually use them!