Would there be a downside to having collisions occur only if both front ends see a collision? If so, what would it be?
I understand how it works. 
Yes, there would be. Unlike the current model, players with a higher lag would profit from it as they would have a much lower probability to be in a collision at all.
To illustrate (with numbers made up on the fly, just to show the principle)
Player A: Ping/Lag 30
Player B: Ping/Lag 30
Player C: Ping/Lag 300
Player A and Player B are about to collide. Total lag is very small, so collision is seen on both FE's - CRASH
Player A and Player C are about to collide. Total lag is quite high, so collision is NOT seen on both FE's - wuuush, no crash
Player A and B have a high chance of being part in collisions, player C does not. This is unfair and has a big impact on flying tactics - player C can fly through enemy planes guns blazing with low risk, 'great' for killing bombers.