Even with the 1 in 10000 false negative rate, I bet someone is doing the cost calculation of risk vs how many hours it would take for a doctor to check 10000 scans. Doctors themselves are not perfect so they may even have a higher error rate.
Give the doctor an AI tool which is fast and 99.999% accurate. Since they have automation now, give them a massive workload, so they can’t reasonably check everything. Now the machine does the work and the doctor is just the fall-guy if it messes up.