As you've noted, Bayes' Theorem is just a straight forward result of probability calculus. In that light, it is entirely uncontroversial.
What people really seem to get excited about is Bayesianism, which is something more than just the application of Bayes' Theorem.
To understand people's interest in Bayesianism, I think you then need to distinguish its use in two types of applications: how we use probabilities to deal with uncertainty when drawing inferences from data generated by scientific studies (i.e. statistical inference); and whether hum...
Another key work here is Probability Theory: The Logic of Science by ET Jaynes. (you can download the entire book here). The early chapters are focused on deriving the probability calculus from logic.