Cobra,
I believe sharing responsibility is simply not possible. It is a good system that the one who wants to make money and the one executing the flight are not the same person. That fact alone increases safety ba far - look at airliner and corporate accident rates.
So the go-nogo decision is best left to the Captain (I would quit my job if it was taken from me).
Of course responsibility in technical matters is shared. Just look at the Spanair accident from last year, two Tecs are still under accusation. It just won't help the pilots anymore - again proof there is just no way of changing the existing system here. It is a logical AND descicion: The CPT AND the TEC who signs the release both have to agree on go for the flight to go ahead.
Then there are the legal matters you are refering to:
newborns on the flight
Well, you could give that responsibility to somebody else, as it is a mere administrative task. But the fact that no police is on board (on a regular basis) empowers the CPT also with the police responsibilities and powers - maintaining order and law aboard, being able to arrest someone, decide to offload, ....
And this actually includes parts of the powers of a judge. Like arresting is a delegation of issuing an arrest warrant from a judge to the police. If danger is imminent or a crime obvious (it will say something similar in every decent countrie's law books) police is allowed to arrest first, then ask the judge the next day or so, but he/she will be asked to uphold arrest or dismiss the arrested.
In an airplane I could give up those responsibilities (and I do, whenever Air Marshalls are on board), but to do so on a regular basis would require police on board at all times. And an administrative clerk plus a navigator to record and fix the position of place of birth, in your example.
Quite impractical, I'd say. They didn't even do this on sail ships a hundred years ago.
And not regulating these matters would lead to a grey area legally, or a law-free zone on an aircraft. I sure wouldn't want to take that ride, neither as crew nor as passenger. An invitation to anarchy and chaos.
So for the physical removal of an aircraft from the ground to the air, where no authorities can be calles upon, all these powers and responsibilities shall be mine, and mine alone, until I delegate them, by my own will.
Nic