BA wants the status quo. That is why they are pushing so hard for a "comprehensive" agreement - meaning complete, meaning unachievable - to kick the ball out of touch for as long as possible. This means they can continue to use their restricted access to LHR to keep fares high. Incidentally, suppose there was much more access to LHR - what do you think would happen? My guess is that airlines would stop making money on business routes to the US, and the number of connections at LHR (which is what make it so attractive to business travellers in the first place - let's face it, it has few other redeeming features!) would fall.
With regard to UA, who do you think is the dominant airline in Star? I'll give you a clue, it's not SAS.
"However, due to travel patterns, for every one destination a US carrier serves in europe, that corresponding country's carrier serves 2-4 in the US. Case in point, SAS serves three US destinations, where as no US carrier serves Copnhagen"
These two sentences are meaningless. Do you mean, "If a US airline flies to city XXX, then the flag carrier that is based in city XXX will fly to 2-4 US cities"? I think that's kind of what you mean. If so, this says nothing about the level-ness of playing fields or otherwise. I mean, it wouldn't surprise me if the reverse applies as well - "If a EU airline flies to city YYY in the US, then a US airline will fly from there to 2-4 EU cities."
I know that people in the States have got used to justifying anything by reference to 9/11 - but why should US airlines have received subsidies as a result? Before you answer that, bear in mind that European airlines generally don't receive subsidies now - certainly nothing like the billions of dollars that were thrown at US carriers in the last couple of years - and didn't as a result of 9/11. There are countries who have lost their flag carriers since then whilst all the dinosaur US carriers - not flag carriers, just businesses exploiting their dominant market position and fortuitous location - are still lumbering along.
"Lack of passengers" - low cost airlines make their own passengers! Or do you think that we - or the federal government - should pay US airlines to operate on more routes that they can't make profitable?