If the goal is to have an automated system to reverse engineer PCBs, that's certainly an interesting and challenging problem.
I think trying to probe the entire thing at once is a non-starter. You'd have to built a custom jig with thousands of extremely precisely placed pogo pins for every unique board you want to probe. This alone would probably make it not cost effective in money or labor.
That brings you to a flying probe machine, that can probe selected points on a board very quickly. How many pads are on a motherboard? I'm guessing at least 5000 easily. If you want to check resistance between each pad and the other 4999 pads, that's something like 5000*5000 = 25 million measurements. Let's cut that in half since there will be many duplicates from ground pins and others, and you don't need to duplicate measurements on already measured nets. So 12.5 million measurements. Let's say a flying probe machine can do 10 measurements per second. This means it will take 14.5 days to probe out an entire board. That's a long time but at least it isn't years. Although if you double the number of pads on the board, the time will quadruple.
If you applied some intelligence to the probing strategy, you could probably reduce the measurement count somewhat. (CPU socket usually has many traces going to DRAM channels and PCIe channels. Check GND and power nets first using known ATX power connector pinouts.)
You'd also need some very fancy computer vision to let a flying probe machine know where to probe just from a picture of a board. Also, the board would probably need to be stripped of all components for probing. A mechanical process like this will always be more error prone than something without moving parts.
It might be easier to strip all the components off the board, get a high-resolution CT scan of it, and then design some very sophisticated software to analyze the copper connections and generate the PCB net list from that. As a bonus, you could probably take it a step further and have your fancy software recreate the PCB in gerber format or other PCB software.
If you want to get on the AI hype-train, then you could design and train an AI model to convert the net lists into schematics. The output wouldn't be perfect, but it would be much faster than manually laying out a schematic from a netlist of thousands of components.
Identifying the components on the board is another problem as others mentioned.
If you haven't done any of this before, I would consider that it might take years to accomplish this. Is it worth it?