We should be equally worried about being overly dependent on clinical methods (human judgment) for important decision making. When looking at an algorithm, you can at least see how it works. Not so easy for "trust me, I'm a doctor, I know what I'm doing."
Check out classic papers like The Robust Beauty of Improper Linear Models or Paul Meehl's work on clinical vs. statistical expertise.
I still don't trust them. Only 15% of doctors get this question right:
>1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
Check out classic papers like The Robust Beauty of Improper Linear Models or Paul Meehl's work on clinical vs. statistical expertise.