Just to add to your post, the reason that there are multiple ways to "center something" is because tables and flexboxes have different behaviors, especially for multiple children, and the third case of arbitrary translation, but all can be made to give the same visual effect here -- the specific case of aligning and valigning a single child to the center of the parent.

In my experience though, the flexbox model is the only example of DWIM in the majority of cases (the only surprise I've had was some situation with an overflowed child inside of a flexbox and requiring an explicit min-height: 0 [1]... something that seemed unintuitive, but modern browsers are beginning to support uniformly).

[1] https://code.google.com/p/chromium/issues/detail?id=506893