The Commission believes that Europe gives too much away and gets too little in return each time one of these deals is agreed. Overly dominant US carriers get yet more access to Europe while their own skies, the biggest single aviation market in the world, remain closed to European carriers.
Let us negotiate European Union-wide agreements on behalf of all member states and we will fly back from the US with a much better deal, goes the Kinnock argument.
A growing number of member states do not agree. They regard decisions about who may take-off and land from their hub airports - a highly lucrative right - as the province of national governments. Mr Kinnock retorts that since Europe is now a single aviation market it should negotiate as one.
The reality, however, is that it remains a market carved up by flag carrying airlines from each member state, all of whom guard their territory fiercely. Side by side with each new open skies bilateral comes an alliance pact between the relevant European flag carrier and one of the big US airlines.
Mr Kinnock has now run out of patience and has sent a "reasoned" opinion to the UK and seven other member states ruling that such agreements infringe EU law. The member states have two months to study the ruling before Mr Kinnock drags them off to the European Court of Justice.
Unfortunately, both he and they know that it will take at least three years before the court delivers its verdict, by which time the horse will almost certainly have bolted. The UK, for instance, is on the point of signing an open skies pact with the US which is tied to approval of the British Airways-American Airlines alliance. This will allow five more US carriers into Heathrow but only one new UK carrier across the Atlantic. Mr Kinnock knows he is running out of time. He's making a lot of noise but probably to not much effect.