1st.. lets establish that current day slow waltz is a bye product of the original Waltz...
What happened next ?. The social BR genre decided they needed a slower version, hence todays result.
Both sides of the Atlantic took a slightly different approach.
The English being also pragmatic, thought commencing with different fot for L and R turns . The Americans also took a pragmatic approach in their view, and decided it would make more sense if ALL dances commenced for the man on the L. foot
One may argue that a closed change preceding a Nat. turn is prep step, but, it is a step in its own right. Look at it this way; at the conclusion of a reverse turn to commence a natural turn one then needs to dance a closed change .
The more interesting thing about Waltz is that prior to modern waltz, only natural turns were used
All of the above theories are really geared towards how a beginner is taught, and each has its merits .