We're planning an upcoming split stay (3 nights at BC/2 nights at Poly),and I think a split stay works perfectly with how my family travels.
How much of a "pain" it is can depend, among other things, on your packing/unpacking style, since having to pack up and move is about the only inconvenience to a split stay. My family packs light and "unpacks light." By that, I mean that our unpacking ritual consists of unzipping packing cubes of clothes and setting them in drawers, hanging a couple of outfits (only what we'll wear at that particular hotel) in the closet if needed, tossing a laundry sack on the floor of the closet to accept dirty clothes at the end of each day, setting a cube of breakfast/snack foods next to the coffeemaker, and putting our toiletry cases under the vanity. We don't tend to spread out and occupy every nook and cranny of the room, and we don't bring enough with us that we could even hope to do that. As a result, re-packing our stuff at the end of our stay takes no more than 10 minutes and as others said, Bell Services will transport your luggage to your next hotel while you go off to a park. That does mean you are "homeless" for a few hours while you wait to check in to your next hotel, although you can still enjoy hotel amenities (pool, etc.) while you wait, as long as you keep the necessary items with you.
Another potential "down-side" is that the Disney dining reservation system will see your two stays as separate for purposes of your 180-day window, meaning you can't make dining reservations for the second half until 180 days from your check-in date for that half. There are ways around this, though -- for our split stay, I made another "dummy" room reservation at a Disney hotel for the same dates as my split stay (but as a single, 5-night stay). That allowed me to make ADRs for the entirety of the split stay at 180 days from our arrival. Then once the 180-day window for the second half of the split stay passed a few days later, I simply canceled the "dummy" reservation without penalty, and the dining reservations (all of which were now within the 180-day window for both halves of the split stay) remained.