I thought that the reason Aerodromes were so named was because the aircraft flown at the time were not able to deal very well with cross winds so a large circular area was used so they could take off and land into wind. These were similar in shape to the venues used for the other popular sport of the day, the Velodrome used for bicycle racing .
From the Latin Dromus - meaning racecourse.
The cousins not being so well up on the classics simply called them Airfields.