Air traffic rights are of course a trade issue of the first order.
The best I could do in finding european statistics to make my point (seems the published stuff I could find is all differences from previous year or sliced in various ways) was an undated paper (presume it is 1999) titled "The European airline Industry: From Single Market to World-Wide Challenges" on the EU web site (europa.eu.int/comm/transport/ais/rules/doc/com.1999 182en.pdf) Table on page 9 states:
Europe Domestic market % of world RPK 7.76%
North America Domestic Market % of world RPK 24.42%
Youse got more bellybuttons but don't fly as much
If anyone in Europe thinks the U.S. is going to give free access to the U.S. domestic market to foreign airlines they are very, very mistaken.