Totally agree with you! Some of my best moments as a math teacher have come from solving the same question in a couple different ways (even when teaching a large class like calculus).

It takes a lot of mathematical knowledge to know how to solve a math problem, but there is something else special that sets the good teachers apart from the average teachers. And I think you hit the nail on the head when you said "there are cases when you can learn the same thing in different ways". I do believe that it is important for educators to know these various ways, know how to teach these different ways, and know how to be able to connect them.