We never stay on site, and have no interest in it. We have at least 10 trips under our belt off property. Not that we have anything against staying on property, it's just of no interest to us. There are so many things we love about staying off site.
We don't have to rely on buses. We can go wherever we want, whenever we want. Want to go from AK to Disney Springs? Easy. Epcot to Blizzard Beach? Just hop in the car. I like driving, so I don't consider it a chore whatsoever. Signs are everywhere, quite easy to follow. Driving around off WDW property is easy too. Any phone GPS will get you where you need to go. Most of the good off site resorts are only 10 minutes away from WDW entrance, so you're not driving far.
This is just a personal thing, but we're huge nutrition and fitness nuts. We could never eat in WDW parks all day, we'd get sick. It's awesome to have a full kitchen that we can have all kinds of food choices for us and the kids. I think a lot of people get the impression that it means spending hours of your vacation slaving over a hot stove. Nothing could be further from the truth. We pick up a lot of cold cuts, frozen foods for the kids (chicken nuggets, Hot Pockets, etc...), and also bulk packages of boneless, skinless chicken breast. We will then throw it in the oven one night while we're relaxing. Takes about 5 minutes to put it in a Pyrex and toss in the over. Voila, we've got food for several days. Yes, there is some "work" involved in doing this, but at least in our opinion, it's so minimal that we don't consider it an issue and it doesn't bother us one bit. We often pack up for the day while we're having our morning coffee. It's become a routine, so it's not stressful whatsoever. We just like having our own food. Outside of buying snacks/desserts, on a 14 day trip, I doubt we buy 3 meals inside WDW. Just not our thing.
Clean towels. Again, not a lot of work. Like at home, we'll use the same towels for several days. All the places we rent provide a lot of towels, so if you really want to switch every day, you could. Doing laundry is so easy. We don't fold or iron really, just wash and go. We pack clothes that specifically don't need ironing and are good with just a wash and go. Again, super simple.
I love not being confined to WDW property. We love to do things off property after a fun day at the park. Souvenir shops, Dunkin Donuts, ice cream shops, etc... Plus, if we need to run to a store to pick up any kind of supplies, it's easy to do.
Most important to us, having the space to spread out. For well under $1000/week, we can rent a 4 bedroom, 2.5 bath townhouse. After a long and fun day at the parks, it's awesome to have room to spread out and relax. The kids love going into "their" room and watching TV or playing on their phones. My wife and I can relax in the family room with a cup of coffee, etc... I think we'd kill each other if we had to spend a week or longer in the same room, especially at bedtime and waking up. Having the comforts of home while on vacation is fantastic.
I have no doubts that there are wonderful things about staying on property, there's a reason so many people do it. But it's not for us, we thoroughly enjoy being off property.