I see problems with the bed of nails and component height, and not just BGA's that pose a problem. QFN packages also have the pads underneath, and there are other components with the connections underneath the component, like some coils, LED's, etc.
Even with pogo pins there can be components in the way for reaching in deep enough to make contact. Flying probes would be a better solution, but it would need a robot arm with good articulation and a long needle to reach in to every nook and granny, and that still leaves BGA's
An X-ray image of the board can be of help, but with multi layer boards it still is a challenge.
Further more it would need automated recognition of components, and that can be difficult too, with the same SMD marking on different components, so knowing the package is also needed, and then still.
Distinguishing a SMD ferrite bead from a SMD capacitor can also be a challenge, and components with very low resistance can mislead the continuity test and make it think there is a direct connection.
Distilling a proper schematic is also not that easy, even with a full node to node list.
So all in al not an easy feat to accomplish.