Speed never matters more than the quality of the surgery. You're conflating constraints and criteria. Speed is sometimes a constraint, but never a criteria.
But speed is a self-imposed constraint on most projects rather than a physical law, meaning it might be violated. Furthermore, there might be a smooth relationship between speed of execution and value returned (even outside of cost of production). So when evaluating how successful a project was (software, surgery, or otherwise), you often do want to use speed as a criterion, even if you initially thought of it as a sort of constraint for the sake of simplifying planning.
No they aren't. Constraints are necessary but not sufficient. Criteria are necessary and sufficient. In other words, necessity is a lower bound and sufficiency is an upper bound. Criteria is the upper bound, constraints are the lower bound.