Trap as we know it evolved from live pigeon trap shooting, a very demanding game where the close first shot at a fast wild bird called for an more open choke and the second shot if required needed to be as full as possible to kill the bird instantly and drop it within the boundary. Double barrelled shotguns evolved to have different fixed chokes in each barrel for different shooting ranges and presentations. These are the guns that were used for clay target trap shooting for generations and they were perfect for the job. In clay bird trap as we shoot it now the presentaions are the same as they were 50 or 100 years ago and the standard Modified and Full combination still works perfectly, Modified at closer ranges for those who shoot quick , 20-22 yards at handicap and first shot on doubles and full for those that wait out the 16 yard birds, have longer handicaps and for the second shot on doubles, which will be at a longer distance than the first bird. The right barrel on a side by side was normally made with the more open choke and this transposed to the bottom barrel on over/unders as they came into use, hence most shooters shot better scores at the closer ranges with the more open bottom barrel and this became the norm. When removable interchageable choke tubes came into use in the 80's they offered great versatiliy to hunters but no real advantage to trap and skeet shooters with guns dedicated to just one of these. To this day there are a gazillion fixed choke trap and skeet guns (not interchageable) in use by satisfied owners and you can still buy new high end fixed choke trap and skeet guns. These older fixed choke guns are 100% competitive in their discipline today but those trap guns and skeet guns are not interchangeable. The introduction of the game of sporting clays really pushed the versatility of choke tubes and a good sporting clays gun can be competitive at trap and skeet - all with one gun.
Having examined many quality trap guns, some doubles but some top singles or bottom singles with 50,000, 100,000 and more rounds through them I can't see any differences in wear that could be attributed to which barrel gets the most use. As for recoil, theoretically the top barrel can rotate upwards more and in a long match some people may eventually feel the difference on the cheek bone if they only use that barrel, I never have. I suppose the bottom then top sequence MAY enable slightly faster target aquisition of the second target in doubles. If recoil is a problem lighten your shot load, lower your velocity or buy a heavier gun.