that is an algorithm for a different problem; here we are looking for a zero, not an extremum, and we want to find all the zeroes (in a two-dimensional plane, so there are usually infinitely many zeroes), not just one of them
perhaps there is a way to apply it to this problem that is obvious to you but not to me
with autodiff we can use a zero-finding algorithm (even one that isn't derivative-free) to find extrema, but i don't know how you'd go about using an extremum-finding algorithm to find zeroes. the first step would seem to be quadrature? but that sounds impractical
as i understand it, the advantage of golden-section search is that, to search for a minimum rather than a zero, you need to in some sense interpolate a parabola rather than a line, so you need three points rather than two, and you'd like them to be somewhat evenly spaced. i don't fully understand why the golden section is better for this than just dividing the interval between the two lowest points in half, but it's definitely an algorithm to solve a different problem
