We've done all kinds of split stays for a number of reasons.
One reason is to save $, especially at current WDW pricing. Onsite perks work for park touring, but MANY Florida resorts boast better pools, far better food, and MUCH lower rates! I hate to say it, but they NOW offer better service! Disney used to be a good value. Not now. I'm tired of being squeezed for every dime, and zero flexibility dining.
Sometimes we've split WDW value resorts with deluxes/offsite especially first/last night, early/late flights. Sometimes it is a matter of promo rate dates. Maybe I can save a ton by flying down a day early, or staying an extra 12 hours.
We also fly into other FL airports. We love Tampa, and save $ spending a day there. Outside rush hour, the drive is only 40min extra. (75 min. TPA to WDW, vs. 30 from MCO) The Tampa area beaches are beautiful! Eating TS meals when we want is a BIG plus!
A third reason piggy backs the above- we love exploring beyond the mouse, especially at the current price gouging. Beyond Tampa and Universal, FL has many fun places. Offsite + car=freedom! The Everglades, Ft.Lauderdale, and St Augustine! Offsite eating costs WAY less and tastes WAY better! FL's neighboring states! We stay near Universal to visit US.
Within the mouse, we've also done split stays to get a change of scene, or special amenities: safari view, the BC pool. Sometimes the resort we want is not available the full week.
With a little creative packing, splits are a breeze!