qualified (as in, skilled and capable), and blessed by regulatory oversight are not the same thing. See also, the glut of people who were practicing doctors who cannot call themselves that in the US, because they have not been blessed by completing a residency program, (and are often actively excluded from doing so.)
See also, why a person who knows all the ins and outs of mechanical engineering, cannot call themselves an engineer without passing and attaining the regulatory approvals.
The latter is intended to assure quality in the former.
Your argument also fails to address the reason why the oath of Hippocrates even took off the way it did. Prior to his school of medicine (and more specifically, how his school of medicine REQUIRED the taking of the oath before they would even TEACH you), getting medical treatment was very much a gamble, with many peddlers of knowingly poor quality remedies roaming the countryside doing much more harm than good, and enriching themselves on the suffering of others. The establishment of his order of physicians elevated medicine from untrustworthy palp, to a reputable higher calling that patients could trust. It is very much this trust that enables modern medicine as a practice, and why the tradition of taking the oath persists.
In light of your question about physicians and being presented with a circumstance where they could not operate due to a conflict with their oath, the doctor with the conflict would recuse himself, and insist on not performing the surgery. He might or might not (depending on how his oath is interpreted; If this was a doctor from the Hippocratic school, he would not direct elsewhere, for instance.) direct the patient to another physician that is capable of performing the surgery without violating his tenets. What he should NOT do, is perform the surgery in violation of his oath.
You will find similar oaths, for similar reasons, in many other civically oriented professions, such as being a legal counsel.