You are right about the mathematics and that is not what is being celebrated. The importance is what the identity lets you do with the quantities involved, not the identity.
Write it in the form that shows why:
P(hypothesis | data) = P(data | hypothesis) × P(hypothesis) / P(data)
The left side is what you want and cannot observe: how likely is my explanation, given what I saw. The right side is built from things you can get at: how likely was this data if the explanation were true, and how likely did the explanation seem beforehand.
So the trivial rearrangement converts an unanswerable question into an answerable one. That is the entire fuss. It is a bridge between the direction reasoning naturally runs — from cause to observation — and the direction we actually need it to run — from observation back to cause.
No other one-line identity in the course does anything like that.