I agree this could work, though it would likely create significant inconvenience for the passenger and increase costs — there is a nonzero cost in arranging such a rendezvous, and it is inconvenient for the passenger to transfer themselves and their belongings to the other vehicle.

As you mentioned, even in this case, the drivers may collude and transfer information and the drivers do have partial information about the passenger.

I suspect very few passengers will be willing to spend extra money and time on such a system. In a sense, you can already do it by calling two Ubers (or an uber and lyft).