Capt Wally,
Just a few thoughts as to why large transport aircraft don't do ASEPTA and singles do.
1 - Transport category aircraft must be able to cope with an engine failure at any stage of the flight and be able to climb to safety or stop within the remaining runway. The ability to out climb the terrain is not a LEGAL consideration for a light twin.
2 - A large transport aircraft would generally not meet the ASEPTA performance requirement to be able to glide to a suitable aerodrome for the required percentages / times of the flight, except possibly along the eastern seaboard in Australia.
3 - I don't think a turn back would be possible - it would be interesting watching someone attempt a 45deg angle of bank turn to return to the airport following a complete propulsion system failure at 700 feet in a heavy.
4 - Off airport landing ability. Singles (including large ones) often land on unprepared surfaces without causing major damage to either the aircraft or the surroundings. The results of transport aircraft landing off airport are generally spectacular.
5 - The same reason we have so many windows in an airliner - too many of the public would refuse to fly otherwise.
Now (ducking for cover) by adding a second engine we increase the risk of an accident during the critical take off phase by doubling the probability of a propulsion system failure when there may be no possible safe outcome (eg short strip / high terrain / heavy load). On this basis it is quite possible that certain routes could be safer flown ASEPTA than in a twin turbo prop.
W