Why does the Turing Machine allow for multiple final states?
I've never seen a definition of Turing machines that allows multiple final states. All the definitions I've seen either have a single "halt" state or one "halt and accept" state and one "halt and reject" state.

There's no benefit to having multiple final states, though there's no real harm, either. In a finite automaton, it makes sense to have multiple final states because the automaton terminates when it runs out of input and whether or not the last state is final determines whether or not it accepts its input. (I prefer the term "accepting state", for this reason.)  But, for Turing machines, the machine halts precisely when it enters a final state, regardless of what's happening on the state.  So, if you have a Turing machine with multiple final states, you could just delete all but one of them and rewrite the transition function to jump to the one that remains, instead of the ones that were deleted.