There is some way to go on this. One needs a really complete procedure depiction before one can do it totally automatically.
For example, (as mentioned above) a typical SID is a straight ahead climb to some altitude, or VOR radial, etc, but not to any database waypoint. So that SID cannot be flown hands-off, for several reasons some of which are pretty nontrivial in certification terms. So, I fly a SID using its chart representation/description, and throw in GPS database waypoints where there are some defined. This is pretty easy but the best one can do automation-wise is to fly on the autopilot in HDG mode - initially at least.
Even if one had full automatic departure/go-around capability, issues remain for GA aircraft, like a minimum climb gradient (for obstacle clearance) which might be tough though possible to achieve, but which cannot be achieved on a given day due to engine management issues (max CHT) which require an early transition to a higher speed, at the expense of climb gradient. I have certainly been to airports where this is an issue. Somehow I don't see the CHT being introduced into the autopilot
Approaches are already possible "fully automatic" with 20 year old kit, and arguably that is where automation is most important for safety. Enroute, automation is vital for the pilot getting some rest