I think there is little doubt that even with today's technology, you could build a plane that executes a full flight from parking position to parking position and do a decent job with it.
But Proof of concept is one thing, commercially viable is a different world.
Next to the valid arguments already raised here and obvious safety concerns one thing that gets overlooked is that simply the ground infrastructure is nowhere near supporting such a technology and will probably be not for a forseeable time. Todays Autoland technology requires CAT II/III facilities that only a fraction of airports have in both directions, so either a full automatic plane will be very limited in the area of operation (forget about NAT ETOPS routes) or there would be the need of a huge investment in ILS facilities worldwide to support a full automatic landing capability which I dont really see happening. So whats the alternative? SBAS? Eventually yes but we are still far off for many years in reliably demonstrating that this can be used for full automatic landings. And there is the possibility of signal jamming...
This is problem is also independent of single or no pilot cockpit as supposedly the single pilot is watching the automatics do its job. If the single pilot has to perform the landing because the automatics can't do it then from a redundancy perspective you need the second pilot anyways.
So which plane manufacturer would now pump billions into designing a plane with such limitations beyond their control? In 20 years maybe but now I dont think any.
So full automated planes without pilots in this century? Probably. Eventually technology and infrastructure will be there. In my lifetime? Maybe. In my last 25 years I have in this profession? Surely not.