They have to maintain steady position (impossible for planes).
Also, the weather over the Channel can be quite unforgiving.
Drones are not the end of the line, though. A quick Google search for "hft neutrino" shows how creative these guys could be in their insatiable quests for shaving off microseconds.
Even if they only move at the speed of light, they can travel in a straight line directly through the earth instead of along the curved surface, saving time. The problem is that if neutrinos can pass through the entire earth unimpeded, most of them will pass through your detector on the other side too.
[EDIT] Or there are the Facebook planes: http://www.theverge.com/2015/7/30/9074925/facebook-aquila-so...