Now that's an excellent question. Many issues arise. Which job is more readily automated? You only need look at in-trail climb, or the new Heathrow vectoring advice thingy (someone post here please with its correct name!), plus TCAS, and other systems, to see which job is already being automated.
Also, if the centre guys have a big problem, those of us airborne would probably get onto the ground somewhere without an accident. If the aircraft has no pilot, and runs into difficulty, then it's 'Goodnight Vienna'.
Passengers don't even know about en-route ATC, in the main (how many Joe Publics think an Air Traffic Controller stands on the ramp with a pair of ping-pong bats?), but they'd be seriously worried about boarding an aircraft without two guys in the front wearing white (or blue!) shirts.
I have a feeling that this discussion could get seriously interesting.... Let's keep it going.
vertigo, bear in mind that, in the situation you describe, we will be trying to get the height off rapidly too, because we are on or above the profile. It's only when we're asked to go down early without an explanation or a clear restriction that these problems generally arise.
[ 22 August 2001: Message edited by: NorthernSky ]