I read yor question one way and some of the responses seem to go another way. We generally prefer onsite, but we've done lots of offsite as well.
First, there is much more to the Orlando area than just WDW. Offsite becomes an advantage if we want to go some place other than Disney- like Universal or the beach.
If you are going to have a car either way- then one offset of offsite is parking fees. Either way, if you are driving, you still have to pay for gas. Navigation is perhaps an issue, also how long it takes to get to WDW. Some close offfsite places like Marriott World Center are on par with onsite.
Yes, the offsite dining options can save money. Many are chains. Timing is an issue. It takes time to drive around- so that is less time in Disney parks. offsite it can be easy if you need to buy anything- clothes, medicine, anything.
Grocery store runs become more feasible offsite. It's not worth the drive for $50 of groceries from onsite, IMO. But offsite, Publix might be right next door. Then again...there's an amazing Whole Foods on Sand Lake just off I-4. Most certainly not your typical grocery store. It's a dining destination unto itself; brick oven pizza, fresh sqeezed juice bar, HUGE buffets, barista, giant bakery, fresh seafood - lots of health(y) foods.
Much of the offsite hotels stay in business due to business travelers. That is one reason we may stay offsite in the area. Often, if you are staying offsite for a convention - you can extend the discount convention rate. Also, lots of offsite places are big chains with special rates and points rewards programs. So you can redeem your points if you are willing to stay offsite.
I think the other reason to stay offsite is simple variety. Some of the offsite places are amazingly beautiful. I've stayed at every Disney resort. It's fun to explore a new place sometimes. Just like visiting Universal is fun for variety. I like WDW better, but Universal has some excellent attractions. Many offsite places have amazing food options and beautiful pools/water attractions.
One more item...I can stay at the airport Hyatt pretty reasonably. If I have an early morning flight, it's really nice to just roll out of bed and be at the airport -for the sameprice as a mod/value. Plus the place is REALLY nice. You can drop off your car the night before and be done with it. (So there's a few $$)