The author doesn't fail to consider this. In fact, he explicitly claims that general surgeons are highly competent, at least when it comes to performing surgery.

The author mistakenly treats “being a general surgeon” as necessary for “being highly competent at performing surgery,” while in the premises, it’s merely sufficient. He fails to consider the possibility that other doctors may also be highly competent at performing surgery.

The author never claims that a competent doctor guarantees a successful surgery. He just argues that a surgery performed by an incompetent doctor involves highly undesirable risks.

The author concludes that surgery performed by anyone other than a general surgeon involves undesirable risks. But he never claims that the riskiness of a surgery is the only factor in deciding whether to have it.

The author doesn’t claim that competence is the only relevant factor when choosing a doctor. He just argues that a surgery performed by an incompetent doctor involves highly undesirable risks.