We've done split-stays twice, and the reason was simple - money.
In 2009, we had a chance for a longer vacation, and wanted to go to the Space Coast, Clearwater, and Sea World. That's three full days not at Disney, so what's the point in paying the Disney resort premium?? We were staying at SSR and loved every minute of it when we were looking for Disney stuff to do, heading to the parks, my son and I played a (horrible) round of golf, but when your Disney agenda is completed, but the vacation isn't, why pay the extra $$?
If some folks don't like that idea, hey, that's cool. C'est la vie. But we got three (four? Don't remember at the moment) extra "post-Disney" days at a fraction of the on-property price, and stayed at the Residence Inn Seaworld that offered a free buffet breakfast every morning. It was super! Packing up everything to move one time was not nearly such a big deal.