Overall, facilities that handle millions of people tend to have a lot of "standing in line" and the slightest disruptions can mean you'll be standing in line for an extra hour.
That's a complete non-starter for now and the next decades. Fully automated operation for 1-dimensional transport (trains) is a solved issue, for 2D, not so much and most certainly not for 3D.
Even though modern planes are very reliable, too many things can go wrong during flight to leave it to a machine - and for what? Just for bragging rights?