Also, 2 engined aircraft have some limits imposed upon them for flight over water, they need to stay withing X minutes of flight to a suitable airport. Think the regulations are called *ETOPS.
*ETOPS = Engines Turning Or Passengers Swimming
Politics does indeed play a part, the A340 uses French engines supplied by Moulinex. Earlier this year, I was on an Air Jamaica A340 from Heathrow to Kingston and I am sure we ran a red light in Hounslow High St

Thankfully, the larger -600 has good old RR engines.
Interesting point about the 727 and Trident, the Trident 3B had four engines with the extra donkey being housed above the tailpipe of number two. I vaguely recall the spare engine being used to give crews a four engine qualification.
Getting back to the 2 v 4 discussion, all twins tend to look the same these days which makes the world a dull place. Thankfully the A380 looks distinctive....fugly but distinctive