W_P,
As the rules exist today, there are portions of the world where the big twins are hampered and a/c with >2 engines are required.
It's not necessarily the safety heights which are the problem. The ETOPS imposition of a combined engine failure/depressurisation event is what snookers them.
Thus [if MD-11 fans will forgive me], although the B777 family may be the twin of choice in this race, any serious world contender will have the B747-xx?? and A340 family in their arsenal to cover the ETOPS holes.
G'day