I'm not suggesting that a plane couldn't be remote-flown effectively, or that the autopilot isn't capable of doing nearly everything. I don't think any today are capable of doing the takeoff roll on their own, and some essential controls like flaps/etc aren't controlled by the autopilot. Also, I don't believe that most aircraft can handle the necessary mode changes, like moving from following path navigation to switching to a CatIII ILS. There is no reason that couldn't be changed, but there would need to be a few changes.
However, the way aircraft actually operate you'd still need about 2 people per plane at certain points in the flight to be safe. You could certainly have them only control the aircraft at critical points and have them take care of other aircraft while they're in cruise/etc with just occasional check-ins.
The autopilot is perfectly capable of following the programmed course all the way to the ground. The reason you need about two people managing the autopilot is that this planned course can't always be predicted before takeoff. If the crew gets the correct news on approach/runway while they're not too busy before decent then they can take their time programming it into the computer and one person wouldn't have any problems keeping up. However, if the winds shift, or ATC has to deal with traffic, or whatever, and during approach the pilots get directions to switch to some other approach/runway then there is a huge pile of time-critical work to be done. The airplane is moving forward at 250kts (that's more than a mile every 15 seconds) along its previously planned route, the crew has to figure out where the new route is in relation to the current one and how to transition from one to the other. Often the crew will just put the plane on a manual course or direct-to course just to get it moving in the correct general direction while they program in the rest of the course. Anything that gets programmed in needs to be checked, because there could be clouds and mountains and buildings in the area and you don't tell a plane to go anywhere without making sure it is absolutely correct. If there is doubt the pilots might need to do a climb to the regions minimum safe altitude - charts indicate heights that are guaranteed to be free of terrain/obstructions with room for safety so once a plane is above that altitude the only issues are time/convenience and running out of fuel (assuming weather doesn't require the plane to try to land sooner).
A few crashes have happened as a result of pilots not managing changes during critical segments of flight.
Not all of the factors that lead to last-minute changes are preventable. Better automation could probably reduce the impact of traffic, but nothing can prevent a storm from moving through, or winds from changing. So, even if remotely piloted a plane will still need 1-2 people paying attention to it during critical phases of flight. Now, those people probably won't be looking out the window or handing yokes - they'll probably be sitting at computer terminals and touchscreens and such. In fact, route planning/entry/verification could probably be done more effectively from a console designed expressly for that purpose vs a cockpit designed for direct manipulation of control surfaces.