I am guessing a pilotless airliner’s autopilot would have access to the speedbrake just like you, and so would easily follow the VNAV path. Besides, that particular problem is easily solved by giving the aircraft access to more wind data for the descent.
There will always be the odd circumstance where human decision making would beat the computer, but there are currently far more circumstances of human error.
I think the concept of pilotless airliners will be accepted once driverless cars become the norm, but there is still a decade or two left in the human pilot yet.