Diesel8 - your post misses the point in all sorts of ways. Firstly, bmi have the slots at LHR but currently can't fly to anywhere in the US from there - the right for them to fly to one airport would be an improvement.
Next, to the best of my knowledge, there are no restrictions on US carriers operating to anywhere in the UK with the exception of LHR - so if they want to fly to Bristol, Blackpool or Biggin Hill, then they can.
Next, in trade terms, we aren't comparing UK with US, we are comparing EU with US. And whilst AA may only fly to three or four destinations in the UK, they fly to considerably more than that in the EU.
Next, you can't call it a draw when there are definite losers. There are private companies in Europe who have never had subsidies, and never sought them. You are saying that the huge US airlines - privately owned! - ought to be compared to the inefficient products of bureaucracy that are the state airlines in the EU? Privately owned airlines in the EU either survive or disappear - and there have been more than a few that have tried to get into the US market that haven't managed it. bmi is only the latest. Privately owned airlines in the US get state subsidies when they can't turn a profit - and if that isn't enough, then they stop paying their creditors for as long as it takes to sort out their finances again.
In the real world of finance, rather than the protected world that is the US (and secondarily, the restricted world that is Bermuda II), UA would have had to sell assets to survive bankruptcy - in a much more compact shape than before - and some of its best assets are its slots at LHR, which held their value. That would have allowed airlines who thought they could make a go of it to buy them and do something with them. In the real, demand-led world of economics, rather than the supply-led regime that exists at LHR and through Bermuda II, airlines would have to set fares to compete with each other - which would make access to LHR a lot less desirable, anyway - it is only because there is a restricted marketplace that the London-US routes are so lucrative - with business class fares typically 50% higher than comparable unrestricted routes elsewhere in Europe, and oddly enough, almost the same for the four airlines that operate on the routes (according to old British Midland press release).