Lots of reasons!
1) We have APs and visit Disney relatively frequently (or at least it's frequent given our distance from Florida.) We've been to Disney many times as a family of five, so we all have favorites and love to try new resorts. It's part of the fun for us. A split stay allows us to do both in one trip. And it's less risky to try something new if we're returning to an old favorite at the end.
2) Transportation and convenience. We like Disney transportation, but would prefer to reduce the time we spend on buses. As a result, we LOVE to split between a monorail resort and an Epcot resort. We spend more time at MK while staying in a monorail resort and then more time in Epcot and DHS while in the Epcot area.
3) Variety. My husband gets antsy in one resort for an entire week. A split stay allows us to mix it up a bit.
4) At certain times, cost. We went during Easter week this year and stayed at a mod until the spring discount kicked in - then moved to deluxe.
Packing for WDW is pretty easy for us with three boys (t-shirts, jeans/shorts, a couple sweatshirts) and not hard to transfer. And now that I can compare it with packing for a week on the Disney Wonder to Alaska, it's really a breeze! So our last three visits and next two visits are all splits.