I saw it put this way in a talk once. The talk was about integrating evidence from multiple sources to figure out if two biological macromolecules physically interact.

The reason, I think, is that this is a yes or no question. Most of the time, though, Bayes' theorem is used for numerical quantities: H means that a real world quantity X has a particular value x. But try to write it in the odds ratio form for this problem. You have to write probabilities given ~H, probabilities of the evidence just excluding a particular value of X, which is really awkward.