Actually I'd never thought about it that way. Always seemed to me to require and foster greater independence. The HS thing just seemed a waste of time, since you're gonna have to put them together at some stage.
I do understand that lots of people find it useful, so maybe my brain just works in an odd way.
Yes, obviously wasnt a big deal for you.. I wouldnt suggest you think about this too much (nor anyone else that can play the passage fine).. but as an example..
Most people have a tendancy to operate their hands in sync, ie. when LH goes forward, so does RH.. when RH pronates, so does LH.. etc. etc.
So.. take this passage, rev etude.

The square brackets show the physical groupings (or paralell sets), as opposed to the musical ones. Physically, the hands are offset by 1 semiquaver - Not very many people would execute it in that manner if they dove into HT, they'd just group everything in sync.
Learning to coordinate it that way leads to it being a boatload more comfortable, speedy and musical though. Or for a more physical point, it ensures that the thumb-pass/hand position change is done correctly - no tense scrunching of the hand.
*clearly I'm in the mood to throw out opinions that will be disagreeable today
** guarantee this will be misunderstood without an actual demonstration.