I don't think that ST *A OW are chasing after the people looking for $500 tickets from NA to Europe. Look at the arms race to get a better J product on board. The people the alliance carriers are all after are buying $5-10K tickets.
LLC's won't have much downward effect. Now you only need to look at JFK/MXP to see who can have downward pressure on airfares...If the ME3 expands their 5th freedom routes from Europe to the TATL market THAT will cause downward pressure on airfares.