...You don't mention what kind of room you're considering, but if you can snag it, a room with a kitchen would allow you the option of making light breakfasts in the room. That's what we do, and also a big reason we don't do
DDP.
In the three times we've visited SSR, I've not known of any Disney-based food service delivery. ....
No need to try to "snag a room with a kitchen". All the villas at SSR have some sort of kitchen facility. One bedroom and larger have full kitchens (oven, burners, microwave, toaster, dishwasher, full sized refrigerator, dishes, pots and pans, flatware, other utensils). Studios have a kitchenette with a microwave, toaster, undercounter refrigerator with small freezer section, disposable dishes, a few real mugs and glasses. SSR is a timeshare resort of DVC. So it is expected that most guests will use these facilities during their stay. That's why the DVC resorts don't have huge food courts like Value resorts.
Both OKW and SSR do have pizza delivery from Disney. Or you can ask at the front desk (don't call, ask in person, when you call you get the call center that could be in Topeka, KS, Tampa, FL or who knows where). You can also get groceries delivered by Disney or offsite services. You just need to order them ahead of time.
Now if it is pouring down cats and dogs, SSR could be a problem. But otherwise, it's not much different that the GF, Polynesian, any of the moderates or value resorts in walking from your building to the main building.
But if you like a hotel feel, SSR and OKW aren't the place for you. And, in that case, GF and the Polynesian shouldn't be either.
SSR is a very nice resort. It's just not a hotel.